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http://rosettacode.org/wiki/Erd%C3%B6s-Selfridge_categorization_of_primes
Erdös-Selfridge categorization of primes
A prime p is in category 1 if the prime factors of p+1 are 2 and or 3. p is in category 2 if all the prime factors of p+1 are in category 1. p is in category g if all the prime factors of p+1 are in categories 1 to g-1. The task is first to display the first 200 primes allocated to their category, then assign the firs...
#Sidef
Sidef
func Erdös_Selfridge_class(n, s=1) is cached { var f = factor_exp(n+s) f.last.head > 3 || return 1 f.map {|p| __FUNC__(p.head, s) }.max + 1 }   say "First two hundred primes; Erdös-Selfridge categorized:" 200.pn_primes.group_by(Erdös_Selfridge_class).sort_by{.to_i}.each_2d {|k,v| say "#{k} => #{v}" }   ...
http://rosettacode.org/wiki/Erd%C3%B6s-Selfridge_categorization_of_primes
Erdös-Selfridge categorization of primes
A prime p is in category 1 if the prime factors of p+1 are 2 and or 3. p is in category 2 if all the prime factors of p+1 are in category 1. p is in category g if all the prime factors of p+1 are in categories 1 to g-1. The task is first to display the first 200 primes allocated to their category, then assign the firs...
#Wren
Wren
import "./math" for Int import "./fmt" for Fmt   var limit = (1e6.log * 1e6 * 1.2).floor // should be more than enough var primes = Int.primeSieve(limit)   var prevCats = {}   var cat // recursive cat = Fn.new { |p| if (prevCats.containsKey(p)) return prevCats[p] var pf = Int.primeFactors(p+1) if (pf.all {...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#M4
M4
define(`factorial',`ifelse(`$1',0,1,`eval($1*factorial(decr($1)))')')dnl dnl factorial(5)
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#11l
11l
F is_even(i) R i % 2 == 0   F is_odd(i) R i % 2 == 1
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Common_Lisp
Common Lisp
;; 't' usually means "true" in CL, but we need 't' here for time/temperature. (defconstant true 'cl:t) (shadow 't)     ;; Approximates y(t) in y'(t)=f(t,y) with y(a)=y0 and t=a..b and the step size h. (defun euler (f y0 a b h)   ;; Set the initial values and increments of the iteration variables. (do ((t a (+ t h)...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#360_Assembly
360 Assembly
* Evaluate binomial coefficients - 29/09/2015 BINOMIAL CSECT USING BINOMIAL,R15 set base register SR R4,R4 clear for mult and div LA R5,1 r=1 LA R7,1 i=1 L R8,N m=n LOOP LR R4,R7 ...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#ABAP
ABAP
CLASS lcl_binom DEFINITION CREATE PUBLIC.   PUBLIC SECTION. CLASS-METHODS: calc IMPORTING n TYPE i k TYPE i RETURNING VALUE(r_result) TYPE f.   ENDCLASS.   CLASS lcl_binom IMPLEMENTATION.   METHOD calc.   r_result = 1. DATA(i) = 1. ...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#TUSCRIPT
TUSCRIPT
  $$ MODE TUSCRIPT ASK "What fibionacci number do you want?": searchfib="" IF (searchfib!='digits') STOP Loop n=0,{searchfib} IF (n==0) THEN fib=fiba=n ELSEIF (n==1) THEN fib=fibb=n ELSE fib=fiba+fibb, fiba=fibb, fibb=fib ENDIF IF (n!=searchfib) CYCLE PRINT "fibionacci number ",n,"=",fib ENDLOOP  
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#C
C
#include <stdio.h> #include <string.h> #include <locale.h>   typedef int bool; typedef unsigned long long ull;   #define TRUE 1 #define FALSE 0   char as_digit(int d) { return (d >= 0 && d <= 9) ? d + '0' : d - 10 + 'a'; }   void revstr(char *str) { int i, len = strlen(str); char t; for (i = 0; i ...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#MAD
MAD
NORMAL MODE IS INTEGER   R CALCULATE FACTORIAL OF N INTERNAL FUNCTION(N) ENTRY TO FACT. RES = 1 THROUGH FACMUL, FOR MUL = 2, 1, MUL.G.N FACMUL RES = RES * MUL FUNCTION RETURN RES END OF FUNCTION   R USE THE...
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#6502_Assembly
6502 Assembly
  .lf evenodd6502.lst .cr 6502 .tf evenodd6502.obj,ap1 ;------------------------------------------------------ ; Even or Odd for the 6502 by barrym95838 2014.12.10 ; Thanks to sbprojects.com for a very nice assembler! ; The target for this assembly is an Apple II with ; mixed-case output ca...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#D
D
import std.stdio, std.range, std.traits;   /// Approximates y(t) in y'(t)=f(t,y) with y(a)=y0 and t=a..b and the step size h. void euler(F)(in F f, in double y0, in double a, in double b, in double h) @safe if (isCallable!F && __traits(compiles, { real r = f(0.0, 0.0); })) { double y = y0; foreach (immutable t;...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#ACL2
ACL2
(defun fac (n) (if (zp n) 1 (* n (fac (1- n)))))   (defun binom (n k) (/ (fac n) (* (fac (- n k)) (fac k)))
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#Ada
Ada
  with Ada.Text_IO; use Ada.Text_IO; procedure Test_Binomial is function Binomial (N, K : Natural) return Natural is Result : Natural := 1; M  : Natural; begin if N < K then raise Constraint_Error; end if; if K > N/2 then -- Use symmetry M := N - K; else ...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#UNIX_Shell
UNIX Shell
#!/bin/bash   a=0 b=1 max=$1   for (( n=1; "$n" <= "$max"; $((n++)) )) do a=$(($a + $b)) echo "F($n): $a" b=$(($a - $b)) done
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#C.2B.2B
C++
#include <functional> #include <iostream> #include <sstream> #include <vector>   std::string to(int n, int b) { static auto BASE = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";   std::stringstream ss; while (n > 0) { auto rem = n % b; n = n / b; ss << BASE[rem]; }   auto fwd = ss.s...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#MANOOL
MANOOL
  { let rec { Fact = -- compile-time constant binding { proc { N } as -- precondition: N.IsI48[] & (N >= 0)  : if N == 0 then 1 else N * Fact[N - 1] } } in -- use Fact here or just make the whole expression to evaluate to it: Fact }  
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#68000_Assembly
68000 Assembly
BTST D0,#1 BNE isOdd ;else, is even.
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Delphi
Delphi
defmodule Euler do def method(_, _, t, b, _) when t>b, do: :ok def method(f, y, t, b, h) do  :io.format "~7.3f ~7.3f~n", [t,y] method(f, y + h * f.(t,y), t + h, b, h) end end   f = fn _time, temp -> -0.07 * (temp - 20) end Enum.each([10, 5, 2], fn step -> IO.puts "\nStep = #{step}" Euler.method(f, 100....
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Elixir
Elixir
defmodule Euler do def method(_, _, t, b, _) when t>b, do: :ok def method(f, y, t, b, h) do  :io.format "~7.3f ~7.3f~n", [t,y] method(f, y + h * f.(t,y), t + h, b, h) end end   f = fn _time, temp -> -0.07 * (temp - 20) end Enum.each([10, 5, 2], fn step -> IO.puts "\nStep = #{step}" Euler.method(f, 100....
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#ALGOL_68
ALGOL 68
PROC factorial = (INT n)INT: ( INT result;   result := 1; FOR i TO n DO result *:= i OD;   result );   PROC choose = (INT n, INT k)INT: ( INT result;   # Note: code can be optimised here as k < n # result := factorial(n) OVER (factorial(k) * facto...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#UnixPipes
UnixPipes
echo 1 |tee last fib ; tail -f fib | while read x do cat last | tee -a fib | xargs -n 1 expr $x + |tee last done
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#D
D
import std.conv; import std.stdio;   ulong uabs(ulong a, ulong b) { if (a > b) { return a - b; } return b - a; }   bool isEsthetic(ulong n, ulong b) { if (n == 0) { return false; } auto i = n % b; n /= b; while (n > 0) { auto j = n % b; if (uabs(i, j) != 1...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#11l
11l
F eulers_sum_of_powers() V max_n = 250 V pow_5 = (0 .< max_n).map(n -> Int64(n) ^ 5) V pow5_to_n = Dict(0 .< max_n, n -> (Int64(n) ^ 5, n))   L(x0) 1 .< max_n L(x1) 1 .< x0 L(x2) 1 .< x1 L(x3) 1 .< x2 V pow_5_sum = pow_5[x0] + pow_5[x1] + pow_5[x2] + pow_5[x3] ...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#Maple
Maple
  > 5!; 120  
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#8080_Assembly
8080 Assembly
CMDLIN: equ 80h ; Location of CP/M command line argument puts: equ 9h ; Syscall to print a string ;;; Check if number given on command line is even or odd org 100h lxi h,CMDLIN ; Find length of argument mov a,m add l ; Look up last character (digit) mov l,a mov a,m ; Retrieve low digit rar ; Rotate low ...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Erlang
Erlang
  -module(euler). -export([main/0, euler/5]).   cooling(_Time, Temperature) -> (-0.07)*(Temperature-20).   euler(_, Y, T, _, End) when End == T -> io:fwrite("\n"), Y;   euler(Func, Y, T, Step, End) -> if T rem 10 == 0 -> io:fwrite("~.3f ",[float(Y)]); true -> ok end, euler(Func, Y + Step * Func(T, Y), ...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#ALGOL_W
ALGOL W
begin  % calculates n!/k!  % integer procedure factorialOverFactorial( integer value n, k ) ; if k > n then 0 else if k = n then 1 else % k < n % begin integer f; f := 1; for i := k + 1 until...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#APL
APL
3!5 10
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#Ursa
Ursa
def fibIter (int n) if (< n 2) return n end if decl int fib fibPrev num set fib (set fibPrev 1) for (set num 2) (< num n) (inc num) set fib (+ fib fibPrev) set fibPrev (- fib fibPrev) end for return fib end
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#C.2B.2B
C++
#include <primesieve.hpp>   #include <chrono> #include <iomanip> #include <iostream> #include <locale>   class composite_iterator { public: composite_iterator(); uint64_t next_composite();   private: uint64_t composite; uint64_t prime; primesieve::iterator pi; };   composite_iterator::composite_iter...
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#F.23
F#
  // Generate Esthetic Numbers. Nigel Galloway: March 21st., 2020 let rec fN Σ n g = match g with h::t -> match List.head h with 0 -> fN ((1::h)::Σ) n t |g when g=n-1 -> fN ((g-1::h)::Σ) n t |g -> fN...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#360_Assembly
360 Assembly
EULERCO CSECT USING EULERCO,R13 B 80(R15) DC 17F'0' DC CL8'EULERCO' STM R14,R12,12(R13) ST R13,4(R15) ST R15,8(R13) LR R13,R15 ZAP X1,=P'1' LOOPX1 ZAP PT,MAXN do x1=1 to maxn-4 SP ...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#Mathematica_.2F_Wolfram_Language
Mathematica / Wolfram Language
factorial[n_Integer] := n*factorial[n-1] factorial[0] = 1
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#8086_Assembly
8086 Assembly
test ax,1 jne isOdd ;else, is even
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#8th
8th
: odd? \ n -- boolean dup 1 n:band 1 n:= ; : even? \ n -- boolean odd? not ;
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Euler_Math_Toolbox
Euler Math Toolbox
  >function dgleuler (f,x,y0) ... $ y=zeros(size(x)); y[1]=y0; $ for i=2 to cols(y); $ y[i]=y[i-1]+f(x[i-1],y[i-1])*(x[i]-x[i-1]); $ end; $ return y; $endfunction >function f(x,y) := -k*(y-TR) >k=0.07; TR=20; TS=100; >x=0:1:100; dgleuler("f",x,TS)[-1] 20.0564137335 >x=0:2:100; dgleuler("f",x,TS)[-1] 20.042463183...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#F.23
F#
let euler f (h : float) t0 y0 = (t0, y0) |> Seq.unfold (fun (t, y) -> Some((t,y), ((t + h), (y + h * (f t y)))))   let newtonCoolíng _ y = -0.07 * (y - 20.0)   [<EntryPoint>] let main argv = let f = newtonCoolíng let a = 0.0 let y0 = 100.0 let b = 100.0 let h = 10.0 (euler newtonCoolíng...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#AppleScript
AppleScript
set n to 5 set k to 3   on calculateFactorial(val) set partial_factorial to 1 as integer repeat with i from 1 to val set factorial to i * partial_factorial set partial_factorial to factorial end repeat return factorial end calculateFactorial   set n_factorial to calculateFactorial(n) set k_factorial to calculat...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#Ursala
Ursala
#import std #import nat   iterative_fib = ~&/(0,1); ~&r->ll ^|\predecessor ^/~&r sum   recursive_fib = {0,1}^?<a/~&a sum^|W/~& predecessor^~/~& predecessor   analytical_fib =   %np+ -+ mp..round; ..mp2str; sep`+; ^CNC/~&hh take^\~&htt %np@t, (mp..div^|\~& mp..sub+ ~~ @rlX mp..pow_ui)^lrlPGrrPX/~& -+ ^\~& ^(...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#F.23
F#
  // Equal prime and composite sums. Nigel Galloway: March 3rd., 2022 let fN(g:seq<int64>)=let g=(g|>Seq.scan(fun(_,n,i) g->(g,n+g,i+1))(0,0L,0)|>Seq.skip 1).GetEnumerator() in (fun()->g.MoveNext()|>ignore; g.Current) let fG n g=let rec fG a b=seq{match a,b with ((_,p,_),(_,c,_)) when p<c->yield! fG(n()) b |((_,p,_),(_...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#FreeBASIC
FreeBASIC
#include "isprime.bas"   Dim As Integer i = 0 Dim As Integer IndN = 1, IndM = 1 Dim As Integer NumP = 2, NumC = 4 Dim As Integer SumP = 2, SumC = 4 Print " sum prime sum composite sum" Do If SumC > SumP Then Do NumP += 1 Loop Until isPrime(NumP) SumP += NumP...
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#Factor
Factor
USING: combinators deques dlists formatting grouping io kernel locals make math math.order math.parser math.ranges math.text.english prettyprint sequences sorting strings ;   :: bfs ( from to num base -- ) DL{ } clone :> q base 1 - :> ld num q push-front [ q deque-empty? ] [ q pop-back :> st...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#6502_Assembly
6502 Assembly
; Prove Euler's sum of powers conjecture false by finding ; positive a,b,c,d,e such that a⁵+b⁵+c⁵+d⁵=e⁵.   ; we're only looking for the first counterexample, which occurs with all ; integers less than this value max_value = $fa  ; decimal 250   ; this header turns our code into a LOADable and RUNnable BASIC progra...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#MATLAB
MATLAB
answer = factorial(N)
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#AArch64_Assembly
AArch64 Assembly
  /* ARM assembly AARCH64 Raspberry PI 3B and android arm 64 bits*/ /* program oddEven64.s */   /*******************************************/ /* Constantes file */ /*******************************************/ /* for this file see task include a file in language AArch64 assembly*/ .include "...
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#ABAP
ABAP
  cl_demo_output=>display( VALUE string_table( FOR i = -5 WHILE i < 6 ( COND string( LET r = i MOD 2 IN WHEN r = 0 THEN |{ i } is even| ELSE |{ i } is odd| ) ) ) ).  
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Factor
Factor
USING: formatting fry io kernel locals math math.ranges sequences ; IN: rosetta-code.euler-method   :: euler ( quot y! a b h -- ) a b h <range> [  :> t t y "%7.3f %7.3f\n" printf t y quot call h * y + y! ] each ; inline   : cooling ( t y -- x ) nip 20 - -0.07 * ;   : euler-method-demo ( -...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Forth
Forth
: newton-cooling-law ( f: temp -- f: temp' ) 20e f- -0.07e f* ;   : euler ( f: y0 xt step end -- ) 1+ 0 do cr i . fdup f. fdup over execute dup s>f f* f+ dup +loop 2drop fdrop ;   100e ' newton-cooling-law 2 100 euler cr 100e ' newton-cooling-law 5 100 euler cr 100e ' newton-cooling-law 10 10...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#Arturo
Arturo
factorial: function [n]-> product 1..n binomial: function [x,y]-> (factorial x) / (factorial y) * factorial x-y   print binomial 5 3
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#AutoHotkey
AutoHotkey
MsgBox, % Round(BinomialCoefficient(5, 3))   ;--------------------------------------------------------------------------- BinomialCoefficient(n, k) { ;--------------------------------------------------------------------------- r := 1 Loop, % k < n - k ? k : n - k { r *= n - A_Index + 1 r /= A_In...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#V
V
[fib [small?] [] [pred dup pred] [+] binrec].
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Go
Go
package main   import ( "fmt" "log" "rcu" "sort" )   func ord(n int) string { if n < 0 { log.Fatal("Argument must be a non-negative integer.") } m := n % 100 if m >= 4 && m <= 20 { return fmt.Sprintf("%sth", rcu.Commatize(n)) } m %= 10 suffix := "th" if m ...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#J
J
Pn=: +/\ pn=: p: i.1e6 NB. first million primes pn and their running sum Pn Cn=: +/\(4+i.{:pn)-.pn NB. running sum of composites starting at 4 and excluding those primes both=: Pn(e.#[)Cn NB. numbers in both sequences   both,.(Pn i.both),.Cn i.both NB. values, Pn index m, Cn index n 10 2 1 ...
http://rosettacode.org/wiki/Ethiopian_multiplication
Ethiopian multiplication
Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving. Method: Take two numbers to be multiplied and write them down at the top of two columns. In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last ...
#11l
11l
F halve(x) R x I/ 2   F double(x) R x * 2   F even(x) R !(x % 2)   F ethiopian(=multiplier, =multiplicand) V result = 0   L multiplier >= 1 I !even(multiplier) result += multiplicand multiplier = halve(multiplier) multiplicand = double(multiplicand)   R result   print(ethiop...
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#Forth
Forth
\ Returns the next esthetic number in the given base after n, where n is an \ esthetic number in that base or one less than a power of base. : next_esthetic_number { n base -- n } n 1+ base < if n 1+ exit then n base / dup base mod dup n base mod 1+ = if dup 1+ base < if 2drop n 2 + exit then then drop base rec...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#Ada
Ada
with Ada.Text_IO;   procedure Sum_Of_Powers is   type Base is range 0 .. 250; -- A, B, C, D and Y are in that range type Num is range 0 .. 4*(250**5); -- (A**5 + ... + D**5) is in that range subtype Fit is Num range 0 .. 250**5; -- Y**5 is in that range   Modulus: constant Num := 254; type Modular is mod...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#Maude
Maude
  fmod FACTORIAL is   protecting INT .   op undefined : -> Int . op _! : Int -> Int .   var n : Int .   eq 0 ! = 1 . eq n ! = if n < 0 then undefined else n * (sd(n, 1) !) fi .   endfm   red 11 ! .  
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#Action.21
Action!
PROC OddByAnd(INT v) IF (v&1)=0 THEN Print(" even") ELSE Print(" odd ") FI RETURN   PROC OddByMod(INT v)  ;MOD doesn't work properly for negative numbers in Action! IF v<0 THEN v=-v FI IF v MOD 2=0 THEN Print(" even") ELSE Print(" odd ") FI RETURN   PROC OddByDiv(INT v) INT d d=...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Fortran
Fortran
program euler_method use iso_fortran_env, only: real64 implicit none   abstract interface ! a derivative dy/dt as function of y and t function derivative(y, t) use iso_fortran_env, only: real64 real(real64) :: derivative real(real64), intent(in) :: t, y end function end interface   real(real64), param...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#AWK
AWK
  # syntax: GAWK -f EVALUATE_BINOMIAL_COEFFICIENTS.AWK BEGIN { main(5,3) main(100,2) main(33,17) exit(0) } function main(n,k, i,r) { r = 1 for (i=1; i<k+1; i++) { r *= (n - i + 1) / i } printf("%d %d = %d\n",n,k,r) }  
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#Batch_File
Batch File
@echo off & setlocal   if "%~2"=="" ( echo Usage: %~nx0 n k && goto :EOF )   call :binom binom %~1 %~2 1>&2 set /P "=%~1 choose %~2 = "<NUL echo %binom%   goto :EOF   :binom <var_to_set> <N> <K> setlocal set /a coeff=1, nk=%~2 - %~3 + 1 for /L %%I in (%nk%, 1, %~2) do set /a coeff *= %%I for /L %%I in (1, 1, %~3) do se...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#Vala
Vala
  int fibRec(int n){ if (n < 2) return n; else return fibRec(n - 1) + fibRec(n - 2); }  
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#jq
jq
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] +.;   def task($sievesize): {compSums:[], primeSums:[], csum:0, psum:0 } | reduce range(2; $sievesize) as $i (.; if $i|is_prime then .psum += $i | .primeSums += [.psum] else .csum += $i | .compSums += [ .csum ]...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Julia
Julia
using Primes   function getsequencematches(N, masksize = 1_000_000_000) pmask = primesmask(masksize) found, psum, csum, pindex, cindex, pcount, ccount = 0, 2, 4, 2, 4, 1, 1 incrementpsum() = (pindex += 1; if pmask[pindex] psum += pindex; pcount += 1 end) incrementcsum() = (cindex += 1; if !pmask[cindex]...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Perl
Perl
use strict; use warnings; use feature <say state>; use ntheory <is_prime next_prime>;   sub comma { reverse ((reverse shift) =~ s/(.{3})/$1,/gr) =~ s/^,//r } sub suffix { my($d) = $_[0] =~ /(.)$/; $d == 1 ? 'st' : $d == 2 ? 'nd' : $d == 3 ? 'rd' : 'th' }   sub prime_sum { state $s = state $p = 2; state $i = 1; ...
http://rosettacode.org/wiki/Ethiopian_multiplication
Ethiopian multiplication
Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving. Method: Take two numbers to be multiplied and write them down at the top of two columns. In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last ...
#8080_Assembly
8080 Assembly
org 100h jmp demo ;;; HL = BC * DE ;;; BC is left column, DE is right column emul: lxi h,0 ; HL will be the accumulator   ztest: mov a,b ; Check if the left column is zero. ora c ; If so, stop. rz   halve: mov a,b ; Halve BC by rotating it right. rar ; We know the carry is zero here because of the ORA. mov b,...
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#FreeBASIC
FreeBASIC
  dim shared as string*16 digits = "0123456789ABCDEF"   function get_digit( n as uinteger ) as string return mid(digits, n+1, 1) end function   function find_digit( s as string ) as integer for i as uinteger = 1 to len(digits) if s = mid(digits, i, 1) then return i next i return -999 end functio...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#ALGOL_68
ALGOL 68
# max number will be the highest integer we will consider # INT max number = 250;   # Construct a table of the fifth powers of 1 : max number # [ max number ]LONG INT fifth; FOR i TO max number DO LONG INT i2 = i * i; fifth[ i ] := i2 * i2 * i OD;   # find the first a, b, ...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#Maxima
Maxima
n!
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#Ada
Ada
-- Ada has bitwise operators in package Interfaces, -- but they work with Interfaces.Unsigned_*** types only. -- Use rem or mod for Integer types, and let the compiler -- optimize it. declare N : Integer := 5; begin if N rem 2 = 0 then Put_Line ("Even number"); elseif N rem 2 /= 0 then Put_Line ("O...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Futhark
Futhark
  let analytic(t0: f64) (time: f64): f64 = 20.0 + (t0 - 20.0) * f64.exp(-0.07*time)   let cooling(_time: f64) (temperature: f64): f64 = -0.07 * (temperature-20.0)   let main(t0: f64) (a: f64) (b: f64) (h: f64): []f64 = let steps = i32.f64 ((b-a)/h) let temps = replicate steps 0.0 let (_,temps) = loop (t,temps...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Go
Go
package main   import ( "fmt" "math" )   // fdy is a type for function f used in Euler's method. type fdy func(float64, float64) float64   // eulerStep computes a single new value using Euler's method. // Note that step size h is a parameter, so a variable step size // could be used. func eulerStep(f fdy, x, y,...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#BCPL
BCPL
  GET "libhdr"   LET choose(n, k) = ~(0 <= k <= n) -> 0, 2*k > n -> binomial(n, n - k), binomial(n, k)   AND binomial(n, k) = k = 0 -> 1, binomial(n, k - 1) * (n - k + 1) / k   LET start() = VALOF { LET n, k = ?, ? LET argv = VEC 20 LET sz = ?   sz := rdargs("n/a/n/p,k/a/n/p", argv, 20) UNLESS ...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#BBC_BASIC
BBC BASIC
@%=&1010   PRINT "Binomial (5,3) = "; FNbinomial(5, 3) PRINT "Binomial (100,2) = "; FNbinomial(100, 2) PRINT "Binomial (33,17) = "; FNbinomial(33, 17) END   DEF FNbinomial(N%, K%) LOCAL R%, D% R% = 1 : D% = N% - K% IF D% > K% THEN K% = D% : D% = N% - K% WHILE ...
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#VAX_Assembly
VAX Assembly
0000 0000 1 .entry main,0 7E 7CFD 0002 2 clro -(sp) ;result buffer 5E DD 0005 3 pushl sp ;pointer to buffer 10 DD 0007 4 pushl #16 ;descriptor: len of buffer ...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Phix
Phix
with javascript_semantics atom t0 = time() atom ps = 2, -- current prime sum cs = 4 -- current composite sum integer psn = 1, npi = 1, -- (see below) csn = 1, nci = 3, nc = 4, ncp = 5, found = 0 constant limit = iff(platform()=JS?10:11) while found<limit do integer c = compare(ps,cs) -- {-...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Raku
Raku
use Lingua::EN::Numbers:ver<2.8.2+>;   my $prime-sum = [\+] (2..*).grep: *.is-prime; my $composite-sum = [\+] (2..*).grep: !*.is-prime;   my $c-index = 0;   for ^∞ -> $p-index { next if $prime-sum[$p-index] < $composite-sum[$c-index]; printf( "%20s - %11s prime sum, %12s composite sum  %5.2f seconds\n", ...
http://rosettacode.org/wiki/Ethiopian_multiplication
Ethiopian multiplication
Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving. Method: Take two numbers to be multiplied and write them down at the top of two columns. In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last ...
#ACL2
ACL2
(include-book "arithmetic-3/top" :dir :system)   (defun halve (x) (floor x 2))   (defun double (x) (* x 2))   (defun is-even (x) (evenp x))   (defun multiply (x y) (if (zp (1- x)) y (+ (if (is-even x) 0 y) (multiply (halve x) (double y)))))
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#Go
Go
package main   import ( "fmt" "strconv" )   func uabs(a, b uint64) uint64 { if a > b { return a - b } return b - a }   func isEsthetic(n, b uint64) bool { if n == 0 { return false } i := n % b n /= b for n > 0 { j := n % b if uabs(i, j) != 1 { ...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#ALGOL_W
ALGOL W
begin  % find a, b, c, d, e such that a^5 + b^5 + c^5 + d^5 = e^5  %  % where 1 <= a <= b <= c <= d <= e <= 250  %  % we solve this using the equivalent equation a^5 + b^5 + c^5 = e^5 - d^5  %  % 250^5 is 976 562 500 000 -...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#MAXScript
MAXScript
fn factorial n = ( if n == 0 then return 1 local fac = 1 for i in 1 to n do ( fac *= i ) fac )
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#Agda
Agda
even : ℕ → Bool odd  : ℕ → Bool   even zero = true even (suc n) = odd n   odd zero = false odd (suc n) = even n
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#Aime
Aime
if (x & 1) { # x is odd } else { # x is even }
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Groovy
Groovy
def eulerStep = { xn, yn, h, dydx -> (yn + h * dydx(xn, yn)) as BigDecimal }   Map eulerMapping = { x0, y0, h, dydx, stopCond = { xx, yy, hh, xx0 -> abs(xx - xx0) > (hh * 100) }.rcurry(h, x0) -> Map yMap = [:] yMap[x0] = y0 as BigDecimal def x = x0 while (!stopCond(x, yMap[x])) { yMap[x + h...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#Bracmat
Bracmat
(binomial= n k coef .  !arg:(?n,?k) & (!n+-1*!k:<!k:?k|) & 1:?coef & whl ' ( !k:>0 & !coef*!n*!k^-1:?coef & !k+-1:?k & !n+-1:?n ) & !coef );   binomial$(5,3) 10  
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#Burlesque
Burlesque
  blsq ) 5 3nr 10  
http://rosettacode.org/wiki/Fibonacci_sequence
Fibonacci sequence
The Fibonacci sequence is a sequence   Fn   of natural numbers defined recursively: F0 = 0 F1 = 1 Fn = Fn-1 + Fn-2, if n>1 Task Write a function to generate the   nth   Fibonacci number. Solutions can be iterative or recursive (though recursive solutions are generally considered too slow ...
#VBA
VBA
Public Function Fib(ByVal n As Integer) As Variant Dim fib0 As Variant, fib1 As Variant, sum As Variant Dim i As Integer fib0 = 0 fib1 = 1 For i = 1 To n sum = fib0 + fib1 fib0 = fib1 fib1 = sum Next i Fib = fib0 End Function
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Sidef
Sidef
func f(n) {   var ( p = 2, sp = p, c = 4, sc = c, )   var res = []   while (res.len < n) { if (sc == sp) { res << [sp, c.composite_count, p.prime_count] sc += c.next_composite! } while (sp < sc) { sp += p.next_prime! } ...
http://rosettacode.org/wiki/Equal_prime_and_composite_sums
Equal prime and composite sums
Suppose we have a sequence of prime sums, where each term Pn is the sum of the first n primes. P = (2), (2 + 3), (2 + 3 + 5), (2 + 3 + 5 + 7), (2 + 3 + 5 + 7 + 11), ... P = 2, 5, 10, 17, 28, etc. Further; suppose we have a sequence of composite sums, where each term Cm is the sum of the first m composites. C = (4...
#Wren
Wren
import "./math" for Int import "./sort" for Find import "/fmt" for Fmt   var limit = 4 * 1e8 var c = Int.primeSieve(limit - 1, false) var compSums = [] var primeSums = [] var csum = 0 var psum = 0 for (i in 2...limit) { if (c[i]) { csum = csum + i compSums.add(csum) } else { psum = psum ...
http://rosettacode.org/wiki/Ethiopian_multiplication
Ethiopian multiplication
Ethiopian multiplication is a method of multiplying integers using only addition, doubling, and halving. Method: Take two numbers to be multiplied and write them down at the top of two columns. In the left-hand column repeatedly halve the last number, discarding any remainders, and write the result below the last ...
#Action.21
Action!
INT FUNC EthopianMult(INT a,b) INT res   PrintF("Ethopian multiplication %I by %I:%E",a,b) res=0 WHILE a>=1 DO IF a MOD 2=0 THEN PrintF("%I %I strike%E",a,b) ELSE PrintF("%I %I keep%E",a,b) res==+b FI a==/2 b==*2 OD RETURN (res)   PROC Main() INT res   res=EthopianM...
http://rosettacode.org/wiki/Equilibrium_index
Equilibrium index
An equilibrium index of a sequence is an index into the sequence such that the sum of elements at lower indices is equal to the sum of elements at higher indices. For example, in a sequence   A {\displaystyle A} :   A 0 = − 7 {\displaystyle A_{0}=-7}   A 1 = 1 {\displaystyle A_{1}=1} ...
#11l
11l
F eqindex(arr) R (0 .< arr.len).filter(i -> sum(@arr[0.<i]) == sum(@arr[i+1..]))   print(eqindex([-7, 1, 5, 2, -4, 3, 0]))
http://rosettacode.org/wiki/Environment_variables
Environment variables
Task Show how to get one of your process's environment variables. The available variables vary by system;   some of the common ones available on Unix include:   PATH   HOME   USER
#11l
11l
print(os:getenv(‘HOME’))
http://rosettacode.org/wiki/Esthetic_numbers
Esthetic numbers
An esthetic number is a positive integer where every adjacent digit differs from its neighbour by 1. E.G. 12 is an esthetic number. One and two differ by 1. 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour. 890 is not an esthetic number. Nine and zero differ by 9. These examples are n...
#Haskell
Haskell
import Data.List (unfoldr, genericIndex) import Control.Monad (replicateM, foldM, mzero)   -- a predicate for esthetic numbers isEsthetic b = all ((== 1) . abs) . differences . toBase b where differences lst = zipWith (-) lst (tail lst)   -- Monadic solution, inefficient for small bases. esthetics_m b = do diff...
http://rosettacode.org/wiki/Euler%27s_sum_of_powers_conjecture
Euler's sum of powers conjecture
There is a conjecture in mathematics that held for over two hundred years before it was disproved by the finding of a counterexample in 1966 by Lander and Parkin. Euler's (disproved) sum of powers   conjecture At least k positive kth powers are required to sum to a kth power, except for the trivial case...
#Arturo
Arturo
eulerSumOfPowers: function [top][ p5: map 0..top => [& ^ 5]   loop 4..top 'a [ loop 3..a-1 'b [ loop 2..b-1 'c [ loop 1..c-1 'd [ s: (get p5 a) + (get p5 b) + (get p5 c) + (get p5 d) if integer? index p5 s -> ret...
http://rosettacode.org/wiki/Factorial
Factorial
Definitions   The factorial of   0   (zero)   is defined as being   1   (unity).   The   Factorial Function   of a positive integer,   n,   is defined as the product of the sequence: n,   n-1,   n-2,   ...   1 Task Write a function to return the factorial of a number. Solutions can be iterat...
#Mercury
Mercury
:- module factorial.   :- interface. :- import_module integer.   :- func factorial(integer) = integer.   :- implementation.   :- pragma memo(factorial/1).   factorial(N) = ( N =< integer(0) -> integer(1)  ; factorial(N - integer(1)) * N ).
http://rosettacode.org/wiki/Even_or_odd
Even or odd
Task Test whether an integer is even or odd. There is more than one way to solve this task: Use the even and odd predicates, if the language provides them. Check the least significant digit. With binary integers, i bitwise-and 1 equals 0 iff i is even, or equals 1 iff i is odd. Divide i by 2. The remainder equals...
#ALGOL_68
ALGOL 68
# Algol 68 has a standard operator: ODD which returns TRUE if its integer # # operand is odd and FALSE if it is even # # E.g.: #   INT n; print( ( "Enter an integer: " ) ); read( ( n ) ); print( ( whole( n, 0 ), " is "...
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Haskell
Haskell
-- the solver dsolveBy _ _ [] _ = error "empty solution interval" dsolveBy method f mesh x0 = zip mesh results where results = scanl (method f) x0 intervals intervals = zip mesh (tail mesh)
http://rosettacode.org/wiki/Euler_method
Euler method
Euler's method numerically approximates solutions of first-order ordinary differential equations (ODEs) with a given initial value.   It is an explicit method for solving initial value problems (IVPs), as described in the wikipedia page. The ODE has to be provided in the following form: d y ( t ) d t = f...
#Icon_and_Unicon
Icon and Unicon
  invocable "newton_cooling" # needed to use the 'proc' procedure   procedure euler (f, y0, a, b, h) t := a y := y0 until (t >= b) do { write (right(t, 4) || " " || left(y, 7)) t +:= h y +:= h * (proc(f) (t, y)) # 'proc' applies procedure named in f to (t, y) } write ("DONE") end   procedure newto...
http://rosettacode.org/wiki/Evaluate_binomial_coefficients
Evaluate binomial coefficients
This programming task, is to calculate ANY binomial coefficient. However, it has to be able to output   ( 5 3 ) {\displaystyle {\binom {5}{3}}} ,   which is   10. This formula is recommended: ( n k ) = n ! ( n − k ) ! k ! = n ( n − 1 ) ( n − 2 ) … ( n − k + 1 ) k ( k − 1...
#C
C
#include <stdio.h> #include <limits.h>   /* We go to some effort to handle overflow situations */   static unsigned long gcd_ui(unsigned long x, unsigned long y) { unsigned long t; if (y < x) { t = x; x = y; y = t; } while (y > 0) { t = y; y = x % y; x = t; /* y1 <- x0 % y0 ; x1 <- y0 */ } return x; } ...