Coprime triplets: Difference between revisions
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;Task:
<br>p and q are coprimes if they have no common factors other than 1.
<br> Let '''p, q < 50'''
<br><br>
=={{header|11l}}==
{{trans|Nim}}
<syntaxhighlight lang="11l">V lst = [1, 2]
L
V n = 3
V prev2 = lst[(len)-2]
V prev1 = lst.last
L n C lst | gcd(n, prev2) != 1 | gcd(n, prev1) != 1
n++
I n >= 50
L.break
lst.append(n)
print(lst.join(‘ ’))</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
</pre>
=={{header|Action!}}==
<syntaxhighlight lang="action!">INT FUNC Gcd(INT a,b)
INT tmp
IF a<b THEN
tmp=a a=b b=tmp
FI
WHILE b#0
DO
tmp=a MOD b
a=b b=tmp
OD
RETURN (a)
BYTE FUNC Contains(INT v INT ARRAY a INT count)
INT i
FOR i=0 TO count-1
DO
IF a(i)=v THEN
RETURN (1)
FI
OD
RETURN (0)
BYTE FUNC Skip(INT v INT ARRAY a INT count)
IF Contains(v,a,count) THEN
RETURN (1)
ELSEIF Gcd(v,a(count-1))>1 THEN
RETURN (1)
ELSEIF Gcd(v,a(count-2))>1 THEN
RETURN (1)
FI
RETURN (0)
BYTE FUNC CoprimeTriplets(INT limit INT ARRAY a)
INT i,count
a(0)=1 a(1)=2
count=2
DO
i=3
WHILE Skip(i,a,count)
DO
i==+1
OD
IF i>=limit THEN
RETURN (count)
FI
a(count)=i
count==+1
OD
RETURN (count)
PROC Main()
DEFINE LIMIT="50"
INT ARRAY a(LIMIT)
INT i,count
count=CoprimeTriplets(LIMIT,a)
FOR i=0 TO count-1
DO
PrintI(a(i)) Put(32)
OD
PrintF("%E%EThere are %I coprimes less than %I",count,LIMIT)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Coprime_triplets.png Screenshot from Atari 8-bit computer]
<pre>
1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
There are 36 coprimes less than 50
</pre>
=={{header|ALGOL 68}}==
<syntaxhighlight lang="algol68">BEGIN # find members of the coprime triplets sequence: starting from 1, 2 the #
# subsequent members are the lowest number coprime to the previous two #
# that haven't appeared in the sequence yet #
# iterative Greatest Common Divisor routine, returns the gcd of m and n #
PROC gcd = ( INT m, n )INT:
BEGIN
INT a := ABS m, b := ABS n;
WHILE b /= 0 DO
INT new a = b;
b := a MOD b;
a := new a
OD;
a
END # gcd # ;
# returns an array of the coprime triplets up to n #
OP COPRIMETRIPLETS = ( INT n )[]INT:
BEGIN
[ 1 : n ]INT result;
IF n > 0 THEN
result[ 1 ] := 1;
IF n > 1 THEN
[ 1 : n ]BOOL used;
used[ 1 ] := used[ 2 ] := TRUE;
FOR i FROM 3 TO n DO used[ i ] := FALSE; result[ i ] := 0 OD;
result[ 2 ] := 2;
FOR i FROM 3 TO n DO
INT p1 = result[ i - 1 ];
INT p2 = result[ i - 2 ];
BOOL found := FALSE;
FOR j TO n WHILE NOT found DO
IF NOT used[ j ] THEN
found := gcd( p1, j ) = 1 AND gcd( p2, j ) = 1;
IF found THEN
used[ j ] := TRUE;
result[ i ] := j
FI
FI
OD
OD
FI
FI;
result
END # COPRIMETRIPLETS # ;
[]INT cps = COPRIMETRIPLETS 49;
INT printed := 0;
FOR i TO UPB cps DO
IF cps[ i ] /= 0 THEN
print( ( whole( cps[ i ], -3 ) ) );
printed +:= 1;
IF printed MOD 10 = 0 THEN print( ( newline ) ) FI
FI
OD;
print( ( newline, "Found ", whole( printed, 0 ), " coprime triplets up to ", whole( UPB cps, 0 ), newline ) )
END</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
Found 36 coprime triplets up to 49
</pre>
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">begin % find a sequence of coprime triplets, each element is coprime to the %
% two predeccessors and hasn't appeared in the list yet, the first two %
% elements are 1 and 2 %
integer procedure gcd ( integer value m, n ) ;
begin
integer a, b;
a := abs m;
b := abs n;
while b not = 0 do begin
integer newA;
newA := b;
b := a rem b;
a := newA
end while_b_ne_0 ;
a
end gcd ;
% construct the sequence %
integer array seq ( 1 :: 49 );
integer sCount;
seq( 1 ) := 1; seq( 2 ) := 2; for i := 3 until 49 do seq( i ) := 0;
for i := 3 until 49 do begin
integer s1, s2, lowest;
s1 := seq( i - 1 );
s2 := seq( i - 2 );
lowest := 2;
while begin logical candidate;
lowest := lowest + 1;
candidate := gcd( s1, lowest ) = 1 and gcd( s2, lowest ) = 1;
if candidate then begin
% lowest is coprime to the previous two elements %
% check it hasn't appeared already %
for pos := 1 until i - 1 do begin
candidate := candidate and lowest not = seq( pos );
end for_pos ;
if candidate then seq( i ) := lowest;
end if_lowest_coprime_to_s1_and_s2 ;
not candidate and lowest < 50
end do begin end while_not_found
end for_i ;
% show the sequence %
sCount := 0;
for i := 1 until 49 do begin
if seq( i ) not = 0 then begin
writeon( i_w := 2, s_w := 0, " ", seq( i ) );
sCount := sCount + 1;
if sCount rem 10 = 0 then write()
end if_seq_i_ne_0
end for_i ;
write( i_w := 1, s_w := 0, sCount, " coprime triplets below 50" )
end.</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
36 coprime triplets below 50
</pre>
=={{header|AppleScript}}==
<syntaxhighlight lang="applescript">on hcf(a, b)
repeat until (b = 0)
set x to a
set a to b
set b to x mod b
end repeat
if (a < 0) then return -a
return a
end hcf
on coprimeTriplets(max)
if (max < 3) then return {}
script o
property candidates : {}
property output : {1, 2}
end script
-- When repeatedly searching for lowest unused numbers, it's faster in
-- AppleScript to take numbers from a preset list of candidates which
-- grows shorter from at or near the low end as used numbers are removed
-- than it is to test increasing numbers of previous numbers each time
-- against a list that's growing longer with them.
-- Generate the list of candidates here.
repeat with i from 3 to max
set end of o's candidates to i
end repeat
set candidateCount to max - 2
set {p1, p2} to o's output
set ok to true
repeat while (ok) -- While suitable coprimes found and candidates left.
repeat with i from 1 to candidateCount
set q to item i of o's candidates
set ok to ((hcf(p1, q) is 1) and (hcf(p2, q) is 1))
if (ok) then -- q is coprime with both p1 and p2.
set end of o's output to q
set p1 to p2
set p2 to q
-- Remove q from the candidate list.
set item i of o's candidates to missing value
set o's candidates to o's candidates's numbers
set candidateCount to candidateCount - 1
set ok to (candidateCount > 0)
exit repeat
end if
end repeat
end repeat
return o's output
end coprimeTriplets
-- Task code:
return coprimeTriplets(49)</syntaxhighlight>
{{output}}
<syntaxhighlight lang="applescript">{1, 2, 3, 5, 4, 7, 9, 8, 11, 13, 6, 17, 19, 10, 21, 23, 16, 15, 29, 14, 25, 27, 22, 31, 35, 12, 37, 41, 18, 43, 47, 20, 33, 49, 26, 45}</syntaxhighlight>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">lst: [1 2]
while [true][
n: 3
prev2: lst\[dec dec size lst]
prev1: last lst
while -> any? @[
contains? lst n
1 <> gcd @[n prev2]
1 <> gcd @[n prev1]
] -> n: n + 1
if n >= 50 -> break
'lst ++ n
]
loop split.every:10 lst 'a ->
print map a => [pad to :string & 3]</syntaxhighlight>
{{out}}
<pre> 1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45</pre>
=={{header|C}}==
<syntaxhighlight lang="c">/*
************************
* *
* COPRIME TRIPLETS *
* *
************************
*/
/* Starting from the sequence a(1)=1 and a(2)=2 find the next smallest number
which is coprime to the last two predecessors and has not yet appeared in the
sequence.
p and q are coprimes if they have no common factors other than 1.
Let p, q < 50 */
#include <stdio.h>
int Gcd(int v1, int v2)
{
/* It evaluates the Greatest Common Divisor between v1 and v2 */
int a, b, r;
if (v1 < v2)
{
a = v2;
b = v1;
}
else
{
a = v1;
b = v2;
}
do
{
r = a % b;
if (r == 0)
{
break;
}
else
{
a = b;
b = r;
}
} while (1 == 1);
return b;
}
int NotInList(int num, int numtrip, int *tripletslist)
{
/* It indicates if the value num is already present in the list tripletslist of length numtrip */
for (int i = 0; i < numtrip; i++)
{
if (num == tripletslist[i])
{
return 0;
}
}
return 1;
}
int main()
{
int coprime[50];
int gcd1, gcd2;
int ntrip = 2;
int n = 3;
/* The first two values */
coprime[0] = 1;
coprime[1] = 2;
while ( n < 50)
{
gcd1 = Gcd(n, coprime[ntrip-1]);
gcd2 = Gcd(n, coprime[ntrip-2]);
/* if n is coprime of the previous two value
and it isn't already present in the list */
if (gcd1 == 1 && gcd2 == 1 && NotInList(n, ntrip, coprime))
{
coprime[ntrip++] = n;
/* It starts searching a new triplets */
n = 3;
}
else
{
/* Trying to find a triplet with the next value */
n++;
}
}
/* printing the list of coprime triplets */
printf("\n");
for (int i = 0; i < ntrip; i++)
{
printf("%2d ", coprime[i]);
if ((i+1) % 10 == 0)
{
printf("\n");
}
}
printf("\n\nNumber of elements in coprime triplets: %d\n\n", ntrip);
return 0;
}</syntaxhighlight>
{{out}}
<pre> 1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
Number of elements in coprime triplets: 36</pre>
=={{header|Delphi}}==
{{libheader| System.SysUtils}}
{{Trans|Julia}}
<syntaxhighlight lang="delphi">
program Coprime_triplets;
{$APPTYPE CONSOLE}
uses
System.SysUtils;
//https://rosettacode.org/wiki/Greatest_common_divisor#Pascal_.2F_Delphi_.2F_Free_Pascal
function Gcd(u, v: longint): longint;
begin
if v = 0 then
EXIT(u);
result := Gcd(v, u mod v);
end;
function IsIn(value: Integer; a: TArray<Integer>): boolean;
begin
for var e in a do
if e = value then
exit(true);
Result := false;
end;
function CoprimeTriplets(less_than: Integer = 50): TArray<Integer>;
var
cpt: TArray<Integer>;
_end: Integer;
begin
cpt := [1, 2];
_end := high(cpt);
while True do
begin
var m := 1;
while IsIn(m, cpt) or (gcd(m, cpt[_end]) <> 1) or (gcd(m, cpt[_end - 1]) <> 1) do
inc(m);
if m >= less_than then
exit(cpt);
SetLength(cpt, Length(cpt) + 1);
_end := high(cpt);
cpt[_end] := m;
end;
end;
begin
var trps := CoprimeTriplets();
writeln('Found ', length(trps), ' coprime triplets less than 50:');
for var i := 0 to High(trps) do
begin
write(trps[i]: 2, ' ');
if (i + 1) mod 10 = 0 then
writeln;
end;
{$IFNDEF UNIX} Readln; {$ENDIF}
end.</syntaxhighlight>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// Coprime triplets: Nigel Galloway. May 12th., 2021
let rec fN g=function 0->g=1 |n->fN n (g%n)
let rec fG t n1 n2=seq{let n=seq{1..0x0FFFFFFF}|>Seq.find(fun n->not(List.contains n t) && fN n1 n && fN n2 n) in yield n; yield! cT(n::t) n2 n}
let cT=seq{yield 1; yield 2; yield! fG [1;2] 1 2}
cT|>Seq.takeWhile((>)50)|>Seq.iter(printf "%d "); printfn ""
</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
</pre>
=={{header|Factor}}==
{{works with|Factor|0.99 2021-02-05}}
<
kernel make math prettyprint sequences sets ;
Line 32 ⟶ 525:
50 triplets-upto
[ 9 group simple-table. nl ]
[ length "Found %d terms.\n" printf ] bi</
{{out}}
<pre>
Line 45 ⟶ 538:
=={{header|FreeBASIC}}==
<
if b = 0 then return a
return gcd( b, a mod b )
Line 79 ⟶ 572:
for i as integer = 1 to last
print trips(i);" ";
next i : print</
{{out}}
<pre>
Line 85 ⟶ 578:
1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
</pre>
=={{header|Go}}==
{{trans|Wren}}
{{libheader|Go-rcu}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"rcu"
)
func contains(a []int, v int) bool {
for _, e := range a {
if e == v {
return true
}
}
return false
}
func main() {
const limit = 50
cpt := []int{1, 2}
for {
m := 1
l := len(cpt)
for contains(cpt, m) || rcu.Gcd(m, cpt[l-1]) != 1 || rcu.Gcd(m, cpt[l-2]) != 1 {
m++
}
if m >= limit {
break
}
cpt = append(cpt, m)
}
fmt.Printf("Coprime triplets under %d:\n", limit)
for i, t := range cpt {
fmt.Printf("%2d ", t)
if (i+1)%10 == 0 {
fmt.Println()
}
}
fmt.Printf("\n\nFound %d such numbers\n", len(cpt))
}</syntaxhighlight>
{{out}}
<pre>
Coprime triplets under 50:
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
Found 36 such numbers
</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Data.List (find, transpose, unfoldr)
import Data.List.Split (chunksOf)
import qualified Data.Set as S
--------------------- COPRIME TRIPLES --------------------
coprimeTriples :: Integral a => [a]
coprimeTriples =
[1, 2] <> unfoldr go (S.fromList [1, 2], (1, 2))
where
go (seen, (a, b)) =
Just
(c, (S.insert c seen, (b, c)))
where
Just c =
find
( ((&&) . flip S.notMember seen)
<*> ((&&) . coprime a <*> coprime b)
)
[3 ..]
coprime :: Integral a => a -> a -> Bool
coprime a b = 1 == gcd a b
--------------------------- TEST -------------------------
main :: IO ()
main =
let xs = takeWhile (< 50) coprimeTriples
in putStrLn (show (length xs) <> " terms below 50:\n")
>> putStrLn
( spacedTable
justifyRight
(chunksOf 10 (show <$> xs))
)
-------------------------- FORMAT ------------------------
spacedTable ::
(Int -> Char -> String -> String) -> [[String]] -> String
spacedTable aligned rows =
unlines $
unwords
. zipWith
(`aligned` ' ')
(maximum . fmap length <$> transpose rows)
<$> rows
justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)</syntaxhighlight>
{{Out}}
<pre>36 terms below 50:
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45</pre>
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
'''Preliminaries'''
<syntaxhighlight lang="jq"># jq optimizes the recursive call of _gcd in the following:
def gcd(a;b):
def _gcd:
if .[1] != 0 then [.[1], .[0] % .[1]] | _gcd else .[0] end;
[a,b] | _gcd ;
# Pretty-printing
def nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
n;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
</syntaxhighlight>
'''The task'''
<syntaxhighlight lang="jq">
# Input: an upper bound greater than 2
# Output: the array of coprime triplets [1,2 ... n] where n is less than the upper bound
def coprime_triplets:
. as $less_than
| {cpt: [1, 2], m:0}
| until( .m >= $less_than;
.m = 1
| .cpt as $cpt
| until( (.m | IN($cpt[]) | not) and (gcd(.m; $cpt[-1]) == 1) and (gcd(.m; $cpt[-2]) == 1);
.m += 1 )
| .cpt = $cpt + [.m] )
| .cpt[:-1];
50 | coprime_triplets
| (nwise(10) | map(lpad(2)) | join(" "))</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
</pre>
=={{header|Julia}}==
{{trans|Phix}}
<syntaxhighlight lang="julia">function coprime_triplets(less_than = 50)
cpt = [1, 2]
while true
m = 1
while m in cpt || gcd(m, cpt[end]) != 1 || gcd(m, cpt[end - 1]) != 1
m += 1
end
m >= less_than && return cpt
push!(cpt, m)
end
end
trps = coprime_triplets()
println("Found $(length(trps)) coprime triplets less than 50:")
foreach(p -> print(rpad(p[2], 3), p[1] %10 == 0 ? "\n" : ""), enumerate(trps))
</syntaxhighlight>{{out}}<pre>
Found 36 coprime triplets less than 50:
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[NextTerm]
NextTerm[a_List] := Module[{pred1, pred2, cands},
{pred1, pred2} = Take[a, -2];
cands =
Select[Range[50], CoprimeQ[#, pred1] && CoprimeQ[#, pred2] &];
cands = Complement[cands, a];
If[Length[cands] > 0,
Append[a, First[cands]]
,
a
]
]
Nest[NextTerm, {1, 2}, 120]</syntaxhighlight>
{{out}}
<pre>{1, 2, 3, 5, 4, 7, 9, 8, 11, 13, 6, 17, 19, 10, 21, 23, 16, 15, 29, 14, 25, 27, 22, 31, 35, 12, 37, 41, 18, 43, 47, 20, 33, 49, 26, 45}</pre>
=={{header|Nim}}==
<syntaxhighlight lang="nim">import math, strutils
var list = @[1, 2]
while true:
var n = 3
let prev2 = list[^2]
let prev1 = list[^1]
while n in list or gcd(n, prev2) != 1 or gcd(n, prev1) != 1:
inc n
if n >= 50: break
list.add n
echo list.join(" ")</syntaxhighlight>
{{out}}
<pre>1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45</pre>
=={{header|Perl}}==
{{libheader|ntheory}}
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature <state say>;
use ntheory 'gcd';
use List::Util 'first';
use List::Lazy 'lazy_list';
use enum qw(False True);
use constant Inf => 1e5;
my $ct = lazy_list {
state @c = (1, 2);
state %seen = (1 => True, 2 => True);
state $min = 3;
my $g = $c[-2] * $c[-1];
my $n = first { !$seen{$_} and gcd($_,$g) == 1 } $min .. Inf;
$seen{$n} = True;
$min = first { !$seen{$_} } $min .. Inf;
push @c, $n;
shift @c
};
my @ct;
do { push @ct, $ct->next() } until $ct[-1] > 50; pop @ct;
say join ' ', @ct</syntaxhighlight>
{{out}}
<pre>1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45</pre>
=={{header|Phix}}==
<!--<
<span style="color: #008080;">function</span> <span style="color: #000000;">coprime_triplets</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">less_than</span><span style="color: #0000FF;">=</span><span style="color: #000000;">50</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">cpt</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}</span>
Line 104 ⟶ 842:
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">,{{</span><span style="color: #008000;">"%2d"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">coprime_triplets</span><span style="color: #0000FF;">()})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Found %d coprime triplets:\n%s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)})</span>
<!--</
{{out}}
<pre>
Line 113 ⟶ 851:
47 20 33 49 26 45
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
########################
# #
# COPRIME TRIPLETS #
# #
########################
#Starting from the sequence a(1)=1 and a(2)=2 find the next smallest number
#which is coprime to the last two predecessors and has not yet appeared in
#the sequence.
#p and q are coprimes if they have no common factors other than 1.
#Let p, q < 50
#Function to find the Greatest Common Divisor between v1 and v2
def Gcd(v1, v2):
a, b = v1, v2
if (a < b):
a, b = v2, v1
r = 1
while (r != 0):
r = a % b
if (r != 0):
a = b
b = r
return b
#The first two values
a = [1, 2]
#The next value candidate to belong to a triplet
n = 3
while (n < 50):
gcd1 = Gcd(n, a[-1])
gcd2 = Gcd(n, a[-2])
#if n is coprime of the previous two value and isn't present in the list
if (gcd1 == 1 and gcd2 == 1 and not(n in a)):
#n is the next element of a triplet
a.append(n)
n = 3
else:
#searching a new triplet with the next value
n += 1
#printing the result
for i in range(0, len(a)):
if (i % 10 == 0):
print('')
print("%4d" % a[i], end = '');
print("\n\nNumber of elements in coprime triplets = " + str(len(a)), end = "\n")
</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
Number of elements in coprime triplets = 36</pre>
=={{header|Quackery}}==
<code>coprime</code> is defined at [[Coprimes#Quackery]].
<syntaxhighlight lang="Quackery"> [ over find swap found not ] is unused ( [ x --> b )
' [ 1 2 ] 2
[ 1+ dup 50 < while
over -1 peek
over coprime until
over -2 peek
over coprime until
2dup unused until
join 2 again ]
drop
echo
</syntaxhighlight>
{{out}}
<pre>[ 1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45 ]</pre>
=={{header|Raku}}==
<syntaxhighlight lang="raku"
state %seen = 1, True, 2, True;
state $min = 3;
my $n = ($min .. *).first: { !%seen{$_} && ($_ gcd $
%seen{$n} = True;
if %seen.elems %%
$n
} … *;
put "Coprime triplets
@coprime-triplets[^(@coprime-triplets.first: * > 50, :k)].batch(10)».fmt("%4d").join: "\n";
put "\
@coprime-triplets[
put "\nAnd for the heck of it: 1001st through 1050th Coprime triplet:\n",
@coprime-triplets[1000..1049].batch(10)».fmt("%4d").join: "\n";</syntaxhighlight>
{{out}}
<pre>Coprime triplets
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
Line 137 ⟶ 963:
47 20 33 49 26 45
Or maybe, minimum Coprime triplets that encompass 1 through 50:
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45 53 28 39 55
32 51 59 38 61 63 34 65 57 44
67 69 40 71 73 24 77 79 30 83
89 36 85 91 46 75 97 52 81 95
56 87 101 50 93 103 58 99 107 62
105 109 64 111 113 68 115 117 74 119
121 48 125 127 42
And for the heck of it: 1001st through 1050th Coprime triplet:
682 1293 1361 680 1287 1363 686 1299 1367 688
1305 1369 692 1311 1373 694 1317 1375 698 1323
1381 704 1329 1379 706 1335 1387 716 1341 1385
712 1347 1391 700 1353 1399 710 1359 1393 718
1371 1397 722 1365 1403 724 1377 1405 728 1383</pre>
=={{header|REXX}}==
<
parse arg n cols . /*obtain optional arguments from the CL*/
if n=='' | n=="," then n= 50 /*Not specified? Then use the default.*/
Line 176 ⟶ 1,016:
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
gcd: procedure; parse arg x,y; do until _==0; _= x//y; x= y; y= _; end; return x</
{{out|output|text= when using the default inputs:}}
<pre>
Line 191 ⟶ 1,031:
=={{header|Ring}}==
<
see "working..." + nl
row = 2
Line 240 ⟶ 1,080:
see nl + "Found " + row + " coprime triplets" + nl
see "done..." + nl
</syntaxhighlight>
{{out}}
<pre>
Line 251 ⟶ 1,091:
Found 36 coprime triplets
done...
</pre>
=={{header|RPL}}==
{{works with|HP|49g}}
≪ {2 1} → coprimes
≪ '''WHILE''' coprimes HEAD 50 < '''REPEAT'''
coprimes 1 2 SUB
1
'''DO'''
'''DO''' 1 +
'''UNTIL''' coprimes OVER POS NOT '''END'''
'''UNTIL''' DUP2 GCD {1 1} == '''END'''
'coprimes' STO+ DROP
'''END'''
coprimes TAIL REVLIST
≫ ≫ ‘<span style="color:blue">TASK</span>’ STO
{{out}}
<pre>
1: {1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45}
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">list = [1, 2]
available = (1..50).to_a - list
loop do
i = available.index{|a| list.last(2).all?{|b| a.gcd(b) == 1}}
break if i.nil?
list << available.delete_at(i)
end
puts list.join(" ")
</syntaxhighlight>
{{out}}
<pre>1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func coprime_triplets(callback) {
var (
list = [1,2],
a = 1,
b = 2,
k = 3,
seen = Set()
)
loop {
for (var n = k; true; ++n) {
if (!seen.has(n) && is_coprime(n, a) && is_coprime(n, b)) {
list << n
seen << n
callback(list) && return list
(a, b) = (b, n)
while (seen.has(k)) {
seen.remove(k++)
}
break
}
}
}
}
say "Coprime triplets before first term is > 50:"
coprime_triplets({|list|
list.tail >= 50
}).first(-1).slices(10).each { .«%« '%4d' -> join(' ').say }
say "\nLeast Coprime triplets that encompass 1 through 50:"
coprime_triplets({|list|
list.sort.first(50) == @(1..50)
}).slices(10).each { .«%« '%4d' -> join(' ').say }
say "\n1001st through 1050th Coprime triplet:"
coprime_triplets({|list|
list.len == 1050
}).last(50).slices(10).each { .«%« '%4d' -> join(' ').say }</syntaxhighlight>
{{out}}
<pre>
Coprime triplets before first term is > 50:
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45
Least Coprime triplets that encompass 1 through 50:
1 2 3 5 4 7 9 8 11 13
6 17 19 10 21 23 16 15 29 14
25 27 22 31 35 12 37 41 18 43
47 20 33 49 26 45 53 28 39 55
32 51 59 38 61 63 34 65 57 44
67 69 40 71 73 24 77 79 30 83
89 36 85 91 46 75 97 52 81 95
56 87 101 50 93 103 58 99 107 62
105 109 64 111 113 68 115 117 74 119
121 48 125 127 42
1001st through 1050th Coprime triplet:
682 1293 1361 680 1287 1363 686 1299 1367 688
1305 1369 692 1311 1373 694 1317 1375 698 1323
1381 704 1329 1379 706 1335 1387 716 1341 1385
712 1347 1391 700 1353 1399 710 1359 1393 718
1371 1397 722 1365 1403 724 1377 1405 728 1383
</pre>
Line 256 ⟶ 1,205:
{{trans|Phix}}
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<
import "./
var limit = 50
Line 274 ⟶ 1,221:
}
System.print("Coprime triplets under %(limit):")
System.print("\nFound %(cpt.count) such numbers.")</
{{out}}
Line 286 ⟶ 1,233:
Found 36 such numbers.
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang="xpl0">func GCD(N, D); \Return the greatest common divisor of N and D
int N, D, R; \numerator and denominator
[if D > N then
[R:= D; D:= N; N:= R]; \swap D and N
while D > 0 do
[R:= rem(N/D);
N:= D;
D:= R;
];
return N;
]; \GCD
int A(50), N, I, J;
func Used; \Return 'true' if N is in array A
[for J:= 0 to I-1 do
if A(J) = N then return true;
return false;
];
[A(0):= 1; A(1):= 2;
Text(0, "1 2 ");
I:= 2;
for N:= 3 to 50-1 do
if not Used and
GCD(A(I-2), N) = 1 and
GCD(A(I-1), N) = 1 then \coprime
[A(I):= N; I:= I+1;
IntOut(0, N); ChOut(0, ^ );
N:= 3;
];
]</syntaxhighlight>
{{out}}
<pre>
1 2 3 5 4 7 9 8 11 13 6 17 19 10 21 23 16 15 29 14 25 27 22 31 35 12 37 41 18 43 47 20 33 49 26 45
</pre>
| |||