Frobenius numbers: Difference between revisions
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{{trans|Python}}
<
I v <= 1
R 0B
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L.break
print(n‘ => ’f)
pn = i</
{{out}}
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=={{header|Action!}}==
{{libheader|Action! Sieve of Eratosthenes}}
<
INT FUNC NextPrime(INT p BYTE ARRAY primes)
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FI
OD
RETURN</
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Frobenius_numbers.png Screenshot from Atari 8-bit computer]
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=={{header|ALGOL 68}}==
<
# Frobenius(n) = ( prime(n) * prime(n+1) ) - prime(n) - prime(n+1) #
# reurns a list of primes up to n #
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print( ( " ", whole( frobenius number, 0 ) ) )
OD
END</
{{out}}
<pre>
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=={{header|APL}}==
{{works with|Dyalog APL}}
<
{{out}}
<pre>1 7 23 59 119 191 287 395 615 839 1079 1439 1679 1931 2391 3015 3479 3959 4619 5039 5615 6395 7215 8447 9599</pre>
=={{header|AppleScript}}==
<
if (n < 4) then return (n > 1)
if ((n mod 2 is 0) or (n mod 3 is 0)) then return false
Line 193:
end Frobenii
Frobenii(9999)</
{{output}}
<
=={{header|Arturo}}==
<
frobenius: function [n] -> sub sub primes\[n] * primes\[n+1] primes\[n] primes\[n+1]
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loop split.every:10 chop lst 'a ->
print map a => [pad to :string & 5]</
{{out}}
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=={{header|AutoHotkey}}==
<
loop {
if isprime(i+=2) {
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return false
return true
}</
{{out}}
<pre> 1 7 23 59 119
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=={{header|AWK}}==
<syntaxhighlight lang="awk">
# syntax: GAWK -f FROBENIUS_NUMBERS.AWK
# converted from FreeBASIC
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return(1)
}
</syntaxhighlight>
{{out}}
<pre>
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=={{header|BASIC}}==
<
20 LM = 10000
30 M = SQR(LM)+1
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110 FOR N=0 TO C-2
120 PRINT P(N)*P(N+1)-P(N)-P(N+1),
130 NEXT N</
{{out}}
<pre> 1 7 23 59 119
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=={{header|BASIC256}}==
<syntaxhighlight lang="basic256">
n = 0
lim = 10000
Line 334:
next i
end
</syntaxhighlight>
=={{header|BCPL}}==
<
manifest $( limit = 10000 $)
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writef("%N*N", frob(primes, n))
freevec(primes)
$)</
{{out}}
<pre>1
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=={{header|C}}==
<
#include <stdlib.h>
#include <math.h>
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return 0;
}</
{{out}}
<pre>1
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=={{header|C sharp|C#}}==
Asterisks mark the non-primes among the numbers.
<
class Program {
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if (!flags[j]) { yield return j;
for (int k = sq, i = j << 1; k <= lim; k += i) flags[k] = true; }
for (; j <= lim; j += 2) if (!flags[j]) yield return j; } }</
{{out}}
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=={{header|C++}}==
{{libheader|Primesieve}}
<
#include <iomanip>
#include <iostream>
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}
std::cout << '\n';
}</
{{out}}
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=={{header|Cowgol}}==
<
const LIMIT := 10000;
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print_nl();
n := n + 1;
end loop;</
{{out}}
<pre>1
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8447
9599</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function IsPrime(N: integer): boolean;
{Optimised prime test - about 40% faster than the naive approach}
var I,Stop: integer;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (i + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
function GetNextPrime(Start: integer): integer;
{Get the next prime number after Start}
begin
repeat Inc(Start)
until IsPrime(Start);
Result:=Start;
end;
procedure ShowFrobeniusNumbers(Memo: TMemo);
var N,N1,FN,Cnt: integer;
begin
N:=2;
Cnt:=0;
while true do
begin
Inc(Cnt);
N1:=GetNextPrime(N);
FN:=N * N1 - N - N1;
N:=N1;
if FN>10000 then break;
Memo.Lines.Add(Format('%2d = %5d',[Cnt,FN]));
end;
end;
</syntaxhighlight>
{{out}}
<pre>
1 = 1
2 = 7
3 = 23
4 = 59
5 = 119
6 = 191
7 = 287
8 = 395
9 = 615
10 = 839
11 = 1079
12 = 1439
13 = 1679
14 = 1931
15 = 2391
16 = 3015
17 = 3479
18 = 3959
19 = 4619
20 = 5039
21 = 5615
22 = 6395
23 = 7215
24 = 8447
25 = 9599
</pre>
=={{header|EasyLang}}==
<syntaxhighlight>
fastfunc isprim num .
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
fastfunc nextprim prim .
repeat
prim += 1
until isprim prim = 1
.
return prim
.
prim = 2
repeat
prim0 = prim
prim = nextprim prim
x = prim0 * prim - prim0 - prim
until x >= 10000
write x & " "
.
</syntaxhighlight>
{{out}}
<pre>
1 7 23 59 119 191 287 395 615 839 1079 1439 1679 1931 2391 3015 3479 3959 4619 5039 5615 6395 7215 8447 9599
</pre>
=={{header|Factor}}==
{{works with|Factor|0.99 2021-02-05}}
<
"Frobenius numbers < 10,000:" print
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[ nip dup next-prime ] [ * ] [ [ - ] dip - ] 2tri
dup 10,000 <
] [ . ] while 3drop</
{{out}}
<pre style="height:14em">
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=={{header|Fermat}}==
<
for n = 1 to 25 do !!Frobenius(n) od</
{{out}}
<pre>
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=={{header|FreeBASIC}}==
<
dim as integer pn=2, n=0, f
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pn = i
end if
next i</
{{out}}
<pre>
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25 9599
</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
include "NSLog.incl"
local fn IsPrime( n as long ) as BOOL
long i
BOOL result = YES
if ( n < 2 ) then result = NO : exit fn
for i = 2 to n + 1
if ( i * i <= n ) and ( n mod i == 0 )
result = NO : exit fn
end if
next
end fn = result
void local fn ListFrobenius( upperLimit as long )
long i, pn = 2, n = 0, f, r = 0
NSLog( @"Frobenius numbers through %ld:", upperLimit )
for i = 3 to upperLimit - 1 step 2
if ( fn IsPrime(i) )
n++
f = pn * i - pn - i
if ( f > upperLimit ) then break
NSLog( @"%7ld\b", f )
r++
if r mod 5 == 0 then NSLog( @"" )
pn = i
end if
next
end fn
fn ListFrobenius( 100000 )
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
Frobenius numbers through 100000:
1 7 23 59 119
191 287 395 615 839
1079 1439 1679 1931 2391
3015 3479 3959 4619 5039
5615 6395 7215 8447 9599
10199 10811 11447 12095 14111
16379 17679 18767 20423 22199
23399 25271 26891 28551 30615
32039 34199 36479 37631 38807
41579 46619 50171 51527 52895
55215 57119 59999 63999 67071
70215 72359 74519 77279 78959
82343 89351 94859 96719 98591
</pre>
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<
import (
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}
fmt.Printf("\n\n%d such numbers found.\n", len(frobenius))
}</
{{out}}
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=={{header|Haskell}}==
<
where sieve (x:xs) = x : sieve (filter (\y -> y `mod` x /= 0) xs)
frobenius = zipWith (\a b -> a*b - a - b) primes (tail primes)</
<pre>λ> takeWhile (< 10000) frobenius
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=={{header|J}}==
<
echo frob i. 25</
(Note that <code>frob</code> counts prime numbers starting from 0 (which gives 2), so for some contexts the function to calculate frobenius numbers would be <code>frob@<:</code>.)
{{out}}
<pre>1 7 23 59 119 191 287 395 615 839 1079 1439 1679 1931 2391 3015 3479 3959 4619 5039 5615 6395 7215 8447 9599</pre>
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=={{header|Java}}==
Uses the PrimeGenerator class from [[Extensible prime generator#Java]].
<
public static void main(String[] args) {
final int limit = 1000000;
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return true;
}
}</
{{out}}
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See e.g. [[Erd%C5%91s-primes#jq]] for a suitable implementation of `is_prime`.
<
# specify `null` or `infinite` to generate an unbounded stream.
def frobenius:
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.frob);
9999 | frobenius</
{{out}}
<pre>
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=={{header|Julia}}==
<
const primeslt10k = primes(10000)
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testfrobenius()
</
<pre>
Frobenius numbers less than 1,000,000 (an asterisk marks the prime ones).
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
<
fn[n_] := Prime[n] Prime[n + 1] - Prime[n] - Prime[n + 1]
a = -1;
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If[a < 10^4, AppendTo[res, a]]
]
res</
{{out}}
<pre>{1,7,23,59,119,191,287,395,615,839,1079,1439,1679,1931,2391,3015,3479,3959,4619,5039,5615,6395,7215,8447,9599}</pre>
Line 1,025 ⟶ 1,202:
=={{header|Nim}}==
As I like iterators, I used one for (odd) primes and one for Frobenius numbers. Of course, there are other ways to proceed.
<
func isOddPrime(n: Positive): bool =
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var result = toSeq(frobenius(10_000))
echo "Found $1 Frobenius numbers less than $2:".format(result.len, N)
echo result.join(" ")</
{{out}}
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=={{header|Perl}}==
{{libheader|ntheory}}
<
use warnings;
use feature 'say';
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# process a list with a 2-wide sliding window
my $limit = 10_000;
say "\n" . join ' ', grep { $_ < $limit } slide { $a * $b - $a - $b } @{primes($limit)};</
{{out}}
<pre>25 matching numbers:
Line 1,086 ⟶ 1,263:
=={{header|Phix}}==
<!--<
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">4</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span>
Line 1,102 ⟶ 1,279:
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frob</span><span style="color: #0000FF;">),</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">frob</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">),</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</
{{out}}
<pre>
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=={{header|Python}}==
<
#!/usr/bin/python
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print (n, ' => ', f)
pn = i
</syntaxhighlight>
=={{header|PL/M}}==
<
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
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END;
CALL EXIT;
EOF</
{{out}}
<pre>1
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=={{header|PureBasic}}==
<syntaxhighlight lang="purebasic">
Procedure isPrime(v.i)
If v < = 1 : ProcedureReturn #False
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CloseConsole()
End
</syntaxhighlight>
{{out}}
<pre>
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</pre>
=={{header|Quackery}}==
<code>eratosthenes</code> and <code>isprime</code> are defined at [[Sieve of Eratosthenes#Quackery]].
In this solution the primes and Frobenius numbers are zero indexed rather than one indexed as per the task. It simplifies the code a smidgeon, as Quackery nests are zero indexed.
<syntaxhighlight lang="Quackery"> 200 eratosthenes
[ [ [] 200 times
[ i^ isprime if
[ i^ join ] ] ]
constant
swap peek ] is prime ( n --> n )
[ dup prime
swap 1+ prime
2dup * rot - swap - ] is frobenius ( n --> n )
[] 0
[ tuck frobenius dup
10000 < while
join swap
1+ again ]
drop nip echo </syntaxhighlight>
{{out}}
<pre>[ 1 7 23 59 119 191 287 395 615 839 1079 1439 1679 1931 2391 3015 3479 3959 4619 5039 5615 6395 7215 8447 9599 ]</pre>
=={{header|Raku}}==
<syntaxhighlight lang="raku"
given (^1000).grep( *.is-prime ).rotor(2 => -1)
.map( { (.[0] * .[1] - .[0] - .[1]) } ).grep(* < 10000);</
{{out}}
<pre>25 matching numbers
Line 1,329 ⟶ 1,534:
=={{header|REXX}}==
<
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 10000 /* " " " " " " */
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end /*k*/ /* [↑] only process numbers ≤ √ J */
#= #+1; @.#= j; sq.#= j*j /*bump # Ps; assign next P; P squared*/
end /*j*/; return</
{{out|output|text= when using the default inputs:}}
<pre>
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=={{header|Ring}}==
<
? "working..." + nl + "Frobenius numbers are:"
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s = string(x) l = len(s)
if l > y y = l ok
return substr(" ", 11 - y + l) + s</
{{out}}
<pre>working...
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Found 25 Frobenius numbers
done...</pre>
=={{header|RPL}}==
« → max
« { } 2 OVER
'''DO'''
ROT SWAP + SWAP
DUP NEXTPRIME DUP2 * OVER - ROT -
'''UNTIL''' DUP max ≥ '''END'''
DROP2
» » ‘<span style="color:blue>FROB</span>’ STO
10000 <span style="color:blue>FROB</span>
{{out}}
<pre>
1: { 1 7 23 59 119 191 287 395 615 839 1079 1439 1679 1931 2391 3015 3479 3959 4619 5039 5615 6395 7215 8447 9599 }
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">require 'prime'
Prime.each_cons(2) do |p1, p2|
f = p1*p2-p1-p2
break if f > 10_000
puts f
end
</syntaxhighlight>
{{out}}
<pre>1
7
23
59
119
191
287
395
615
839
1079
1439
1679
1931
2391
3015
3479
3959
4619
5039
5615
6395
7215
8447
9599
</pre>
=={{header|Rust}}==
<
// primal = "0.3"
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}
println!();
}</
{{out}}
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=={{header|Sidef}}==
<
prime(n) * prime(n+1) - prime(n) - prime(n+1)
}
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take(n)
}
}</
{{out}}
<pre>
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=={{header|Wren}}==
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<
import "./
var primes = Int.primeSieve(101)
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}
System.print("Frobenius numbers under 10,000:")
Fmt.tprint("$,5d", frobenius, 9)
System.print("\n%(frobenius.count) such numbers found.")</
{{out}}
Line 1,520 ⟶ 1,776:
=={{header|XPL0}}==
<
int N, I;
[if N <= 1 then return false;
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Text(0, " Frobenius numbers found below 10,000.
");
]</
{{out}}
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=={{header|Yabasic}}==
{{trans|PureBasic}}
<
sub isPrime(v)
if v < 2 then return False : fi
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next i
end
</syntaxhighlight>
{{out}}
<pre>
|