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EKG sequence convergence: Difference between revisions

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EKG sequence convergence (view source)

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;Convergence
If an algorithm that keeps track of the minimum amount of numbers and their corresponding prime factors used to generate the next term is used, then this may be known as the generators essential '''state'''. Two EKG generators with differing starts can converge to produce the same sequence after initial differences.<br>
<code>EKG(N1)</code> and <code>EKG(N2)</code> are said to to have converged at and after generation <code>a(c)</code> ıf the set (unordered collectıon of ıtems) of digıts used so far byif <code>state_of(EKG(N1)</code>.a(c)) and== <code>state_of(EKG(N2)</code> are equal and <code>.a(c))</code> ıs the same for both.
 
 
Line 26:
# Calculate and show here the first 10 members of <code>EKG(10)</code>.
# Calculate and show here at which term <code>EKG(5)</code> and <code>EKG(7)</code> converge &nbsp; ('''stretch goal''').
 
;Extra Credıt:
Fınd the position ın sequence <code>EKG(2)</code> of the 10000th prıme number 104729
 
;Related Tasks:
# [[Greatest common divisor]]
# [[Sieve of Eratosthenes]]
# [[Yellowstone sequence]]
<br>
;Reference:
* [https://www.youtube.com/watch?v=yd2jr30K2R4 The EKG Sequence and the Tree of Numbers]. (Video).
<br><br>
 
=={{header|11l}}==
{{trans|Nim}}
 
<syntaxhighlight lang="11l">F ekg(n, limit)
Set[Int] values
assert(n >= 2)
V r = [(1, 1), (2, n)]
values.add(n)
V i = 3
V prev = n
L i <= limit
V val = 2
L
I val !C values & gcd(val, prev) != 1
values.add(val)
r [+]= (i, val)
prev = val
L.break
val++
i++
R r
 
L(n) [2, 5, 7, 9, 10]
[Int] result
L(i, val) ekg(n, 10)
result [+]= val
print((‘EKG(’n‘):’).ljust(8)‘ ’result.join(‘, ’))
 
V ekg5 = [0] * 101
V ekg7 = [0] * 101
L(i, val) ekg(5, 100) {ekg5[i] = val}
L(i, val) ekg(7, 100) {ekg7[i] = val}
V convIndex = 0
L(i) 2..100
I ekg5[i] == ekg7[i] & sorted(ekg5[1 .< i]) == sorted(ekg7[1 .< i])
convIndex = i
L.break
print(‘EKG(5) and EKG(7) converge at index ’convIndex‘.’)</syntaxhighlight>
 
{{out}}
<pre>
EKG(2): 1, 2, 4, 6, 3, 9, 12, 8, 10, 5
EKG(5): 1, 5, 10, 2, 4, 6, 3, 9, 12, 8
EKG(7): 1, 7, 14, 2, 4, 6, 3, 9, 12, 8
EKG(9): 1, 9, 3, 6, 2, 4, 8, 10, 5, 15
EKG(10): 1, 10, 2, 4, 6, 3, 9, 12, 8, 14
EKG(5) and EKG(7) converge at index 21.
</pre>
 
=={{header|Action!}}==
{{libheader|Action! Tool Kit}}
<syntaxhighlight lang="action!">INCLUDE "D2:SORT.ACT" ;from the Action! Tool Kit
 
BYTE FUNC Contains(BYTE ARRAY a BYTE len,b)
BYTE i
 
IF len=0 THEN
RETURN (0)
FI
FOR i=0 TO len-1
DO
IF a(i)=b THEN
RETURN (1)
FI
OD
RETURN (0)
 
BYTE FUNC Gcd(BYTE a,b)
BYTE 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 AreSame(BYTE ARRAY a,b BYTE len)
BYTE i
 
IF len=0 THEN
RETURN (1)
FI
 
SortB(a,len,0)
SortB(b,len,0)
FOR i=0 TO len-1
DO
IF a(i)#b(i) THEN
RETURN (0)
FI
OD
RETURN (1)
 
PROC CalcEkg(BYTE start,limit BYTE ARRAY ekg)
BYTE len,i
 
ekg(0)=1 ekg(1)=start
FOR len=2 TO limit-1
DO
i=2
DO
IF Contains(ekg,len,i)=0 AND Gcd(ekg(len-1),i)>1 THEN
ekg(len)=i
EXIT
FI
i==+1
OD
OD
RETURN
 
BYTE FUNC CalcConvergence(BYTE ARRAY a,b BYTE len)
BYTE i
 
FOR i=2 TO len-1
DO
IF a(i)=b(i) AND AreSame(a,b,i)=1 THEN
RETURN (i+1)
FI
OD
RETURN (0)
 
PROC PrintSeq(BYTE start BYTE ARRAY ekg BYTE len)
BYTE i
 
PrintF("EKG(%B)=",start)
FOR i=0 TO len-1
DO
IF i>0 THEN Put(32) FI
PrintB(ekg(i))
OD
PrintE("...")
RETURN
 
PROC Main()
DEFINE PTR="CARD"
DEFINE LIMIT="100"
DEFINE SEQCOUNT="5"
DEFINE PART="10"
DEFINE EKG1="1"
DEFINE EKG2="2"
BYTE ARRAY buf(500),starts=[2 5 7 9 10]
PTR ARRAY ekg(SEQCOUNT)
BYTE i,conv
 
Put(125) PutE() ;clear the screen
 
FOR i=0 TO SEQCOUNT-1
DO
ekg(i)=buf+LIMIT*i
CalcEkg(starts(i),LIMIT,ekg(i))
PrintSeq(starts(i),ekg(i),PART)
OD
 
conv=CalcConvergence(ekg(EKG1),ekg(EKG2),LIMIT)
PrintF("%EEKG(%B) and EKG(%B) ",starts(EKG1),starts(EKG2))
IF conv=0 THEN
PrintF("do not converge within %B items",LIMIT)
ELSE
PrintF("converge at index %B",conv)
FI
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/EKG_sequence_convergence.png Screenshot from Atari 8-bit computer]
<pre>
EKG(2)=1 2 4 6 3 9 12 8 10 5...
EKG(5)=1 5 10 2 4 6 3 9 12 8...
EKG(7)=1 7 14 2 4 6 3 9 12 8...
EKG(9)=1 9 3 6 2 4 8 10 5 15...
EKG(10)=1 10 2 4 6 3 9 12 8 14...
 
EKG(5) and EKG(7) converge at index 21
</pre>
 
=={{header|Ada}}==
{{trans|Go}}
<syntaxhighlight lang="ada">with Ada.Text_IO;
with Ada.Containers.Generic_Array_Sort;
 
procedure EKG_Sequences is
 
type Element_Type is new Integer;
 
type Index_Type is new Integer range 1 .. 100;
subtype Show_Range is Index_Type range 1 .. 30;
 
type Sequence is array (Index_Type range <>) of Element_Type;
subtype EKG_Sequence is Sequence (Index_Type);
 
function GCD (Left, Right : Element_Type) return Integer is
A : Element_Type := Left;
B : Element_Type := Right;
begin
while A /= B loop
if A > B
then A := A - B;
else B := B - A;
end if;
end loop;
return Integer (A);
end GCD;
 
function Contains (A : Sequence;
B : Element_Type;
Last : Index_Type) return Boolean
is (for some Value of A (A'First .. Last) => Value = B);
 
function Are_Same (S, T : EKG_Sequence; Last : Index_Type) return Boolean is
S_Copy : Sequence := S (S'First .. Last);
T_Copy : Sequence := T (T'First .. Last);
procedure Sort is
new Ada.Containers.Generic_Array_Sort (Index_Type => Index_Type,
Element_Type => Element_Type,
Array_Type => Sequence);
begin
Sort (S_Copy);
Sort (T_Copy);
return S_Copy = T_Copy;
end Are_Same;
 
function Create_EKG (Start : Element_Type) return EKG_Sequence is
EKG : EKG_Sequence := (1 => 1, 2 => Start, others => 0);
begin
for N in 3 .. Index_Type'Last loop
for I in 2 .. Element_Type'Last loop
-- A potential sequence member cannot already have been used
-- and must have a factor in common with previous member
if not Contains (EKG, I, N)
and then GCD (EKG (N - 1), I) > 1
then
EKG (N) := I;
exit;
end if;
end loop;
end loop;
return EKG;
end Create_EKG;
 
procedure Converge (Seq_A, Seq_B : Sequence;
Term : out Index_Type;
Do_Converge : out Boolean) is
begin
for I in 3 .. Index_Type'Last loop
if Seq_A (I) = Seq_B (I) and then Are_Same (Seq_A, Seq_B, I) then
Do_Converge := True;
Term := I;
return;
end if;
end loop;
Do_Converge := False;
Term := Index_Type'Last;
end Converge;
 
procedure Put (Seq : Sequence) is
use Ada.Text_IO;
begin
Put ("[");
for E of Seq (Show_Range) loop
Put (E'Image);
end loop;
Put ("]");
end Put;
 
use Ada.Text_IO;
EKG_2 : constant EKG_Sequence := Create_EKG (2);
EKG_5 : constant EKG_Sequence := Create_EKG (5);
EKG_7 : constant EKG_Sequence := Create_EKG (7);
EKG_9 : constant EKG_Sequence := Create_EKG (9);
EKG_10 : constant EKG_Sequence := Create_EKG (10);
begin
Put ("EKG( 2): "); Put (EKG_2); New_Line;
Put ("EKG( 5): "); Put (EKG_5); New_Line;
Put ("EKG( 7): "); Put (EKG_7); New_Line;
Put ("EKG( 9): "); Put (EKG_9); New_Line;
Put ("EKG(10): "); Put (EKG_10); New_Line;
 
-- Now compare EKG5 and EKG7 for convergence
declare
Term : Index_Type;
Do_Converge : Boolean;
begin
Converge (EKG_5, EKG_7, Term, Do_Converge);
New_Line;
if Do_Converge then
Put_Line ("EKG(5) and EKG(7) converge at term "
& Term'Image);
else
Put_Line ("EKG5(5) and EKG(7) do not converge within "
& Term'Image & " terms");
end if;
end;
end EKG_Sequences;</syntaxhighlight>
{{out}}
<pre>
EKG( 2): [ 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36]
EKG( 5): [ 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32]
EKG( 7): [ 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32]
EKG( 9): [ 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32]
EKG(10): [ 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32]
 
EKG(5) and EKG(7) converge at term 21
</pre>
 
=={{header|C}}==
{{trans|Go}}
<langsyntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
 
Line 114 ⟶ 419:
printf("\nEKG5(5) and EKG(7) do not converge within %d terms\n", LIMIT);
return 0;
}</langsyntaxhighlight>
 
{{out}}
Line 125 ⟶ 430:
 
EKG(5) and EKG(7) converge at term 21
</pre>
 
=={{header|C++}}==
<syntaxhighlight lang="c++">
 
#include <algorithm>
#include <cstdint>
#include <iomanip>
#include <iostream>
#include <numeric>
#include <vector>
 
void print_vector(const std::vector<int32_t>& list) {
std::cout << "[";
for ( uint64_t i = 0; i < list.size() - 1; ++i ) {
std::cout << list[i] << ", ";
}
std::cout << list.back() << "]" << std::endl;
}
 
bool contains(const std::vector<int32_t>& list, const int32_t& n) {
return std::find(list.begin(), list.end(), n) != list.end();
}
 
bool same_sequence(const std::vector<int32_t>& seq1, const std::vector<int32_t>& seq2, const int32_t& n) {
for ( uint64_t i = n ; i < seq1.size() ; ++i ) {
if ( seq1[i] != seq2[i] ) {
return false;
}
}
return true;
}
 
std::vector<int32_t> ekg(const int32_t& second_term, const uint64_t& term_count) {
std::vector<int32_t> result = { 1, second_term };
int32_t candidate = 2;
while ( result.size() < term_count ) {
if ( ! contains(result, candidate) && std::gcd(result.back(), candidate) > 1 ) {
result.push_back(candidate);
candidate = 2;
} else {
candidate++;
}
}
return result;
}
 
int main() {
std::cout << "The first 10 members of EKG[2], EKG[5], EKG[7], EKG[9] and EKG[10] are:" << std::endl;
for ( int32_t i : { 2, 5, 7, 9, 10 } ) {
std::cout << "EKG[" << std::setw(2) << i << "] = "; print_vector(ekg(i, 10));
}
std::cout << std::endl;
 
std::vector<int32_t> ekg5 = ekg(5, 100);
std::vector<int32_t> ekg7 = ekg(7, 100);
int32_t i = 1;
while ( ! ( ekg5[i] == ekg7[i] && same_sequence(ekg5, ekg7, i) ) ) {
i++;
}
// Converting from 0-based to 1-based index
std::cout << "EKG[5] and EKG[7] converge at index " << i + 1
<< " with a common value of " << ekg5[i] << "." << std::endl;
}
</syntaxhighlight>
{{ out }}
<pre>
The first 10 members of EKG[2], EKG[5], EKG[7], EKG[9] and EKG[10] are:
EKG[ 2] = [1, 2, 4, 6, 3, 9, 12, 8, 10, 5]
EKG[ 5] = [1, 5, 10, 2, 4, 6, 3, 9, 12, 8]
EKG[ 7] = [1, 7, 14, 2, 4, 6, 3, 9, 12, 8]
EKG[ 9] = [1, 9, 3, 6, 2, 4, 8, 10, 5, 15]
EKG[10] = [1, 10, 2, 4, 6, 3, 9, 12, 8, 14]
 
EKG[5] and EKG[7] converge at index 21 with a common value of 24.
</pre>
 
Line 130 ⟶ 510:
===The Function===
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_function Extensible Prime Generator (F#)]
<langsyntaxhighlight lang="fsharp">
// Generate EKG Sequences. Nigel Galloway: December 6th., 2018
let EKG n=seq{
Line 137 ⟶ 517:
((fun e->i.[e]<-i.[e]+e), (fun l->l|>List.map fN))
let fU l= pCache|>Seq.takeWhile(fun n->n<=l)|>Seq.filter(fun n->l%n=0)|>List.ofSeq
let rec EKG l (αα,ββ)=seq{let b=fU ββ in if (ββ=n||ββ<snd((fG b|>List.maxBy snd))) then fN αα; yield! EKG l (fG l|>List.minBy snd)
else fN αα;yield ββ;yield! EKG b (fG b|>List.minBy snd)}
yield! seq[1;n]; let g=fU n in yield! EKG g (fG g|>Seq.minBy snd)}
let EKGconv n g=Seq.zip(EKG n)(EKG g)|>Seq.skip 2|>Seq.scan(fun(n,i,g,e)(l,β)->(Set.add l n,Set.add β i,l,β))(set[1;n],set[1;g],0,0)|>Seq.takeWhile(fun(n,i,g,e)->g<>e||n<>i)
</lang>
</syntaxhighlight>
 
===The Task===
<langsyntaxhighlight lang="fsharp">
EKG 2 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
EKG 3 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
let EKGconv n g=Seq.zip(EKG n)(EKG g)|>Seq.skip 2|>Seq.scan(fun(n,i,g,e)(l,β)->(Set.add l n,Set.add β i,l,β))(set[1;n],set[1;g],0,0)|>Seq.takeWhile(fun(n,i,g,e)->g<>e||n<>i)
EKG 5 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
EKG 7 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
EKG 9 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
EKG 10 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
printfn "%d" (let n,_,_,_=EKGconv 2 5|>Seq.last in ((Set.count n)+1)
</syntaxhighlight>
</lang>
{{out}}
<pre>
1, 2, 4, 6, 3, 9,12, 8,10, 5,15,18,14, 7,21,24,16,20,22,11,33,27,30,25,35,28,26,13,39,36,32,34,17,51,42,38,19,57,45,40,44,46,23,69,48
1, 3, 6, 2, 4, 8,10, 5,15, 9,12,14, 7,21,18,16,20,22,11,33,24,26,13,39,27,30,25,35,28,32,34,17,51,36,38,19,57,42,40,44,46,23,69,45,48
1, 5,10, 2, 4, 6, 3, 9,12, 8,14, 7,21,15,18,16,20,22,11,33,24,26,13,39,27,30,25,35,28,32,34,17,51,36,38,19,57,42,40,44,46,23,69,45,48
45
</pre>
===Extra Credit===
<langsyntaxhighlight lang="fsharp">
prıntfn "%d" (EKG 2|>Seq.takeWhile(fun n->n<>104729) ((Seq.length n)+1)
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 161 ⟶ 549:
Real: 00:10:21.967, CPU: 00:10:25.300, GC gen0: 65296, gen1: 1
</pre>
 
=={{header|Factor}}==
{{works with|Factor|0.99 2019-10-06}}
<syntaxhighlight lang="factor">USING: combinators.short-circuit formatting fry io kernel lists
lists.lazy math math.statistics prettyprint sequences
sequences.generalizations ;
 
: ekg? ( n seq -- ? )
{ [ member? not ] [ last gcd nip 1 > ] } 2&& ;
 
: (ekg) ( seq -- seq' )
2 lfrom over [ ekg? ] curry lfilter car suffix! ;
 
: ekg ( n limit -- seq )
[ 1 ] [ V{ } 2sequence ] [ 2 - [ (ekg) ] times ] tri* ;
 
: show-ekgs ( seq n -- )
'[ dup _ ekg "EKG(%d) = %[%d, %]\n" printf ] each ;
 
: converge-at ( n m max -- o )
tuck [ ekg [ cum-sum ] [ rest-slice ] bi ] 2bi@
[ swapd [ = ] 2bi@ and ] 4 nfind 4drop dup [ 2 + ] when ;
 
{ 2 5 7 9 10 } 20 show-ekgs nl
"EKG(5) and EKG(7) converge at term " write
5 7 100 converge-at .</syntaxhighlight>
{{out}}
<pre>
EKG(2) = { 1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 14, 7, 21, 24, 16, 20, 22, 11 }
EKG(5) = { 1, 5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11, 33 }
EKG(7) = { 1, 7, 14, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 16, 20, 22, 11, 33, 21 }
EKG(9) = { 1, 9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, 33 }
EKG(10) = { 1, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 5, 20, 16, 18, 22, 11, 33 }
 
EKG(5) and EKG(7) converge at term 21
</pre>
 
=={{header|FreeBASIC}}==
{{trans|XPL0}}
As can be seen, EKG(5) And EKG(7) converge at n = 21.
<syntaxhighlight lang="vbnet">Const limite = 30
Dim Shared As Integer n, A(limite + 1)
 
Function Used(m As Integer) As Boolean 'Return 'True' if m is in array A
For i As Integer = 1 To n - 1
If m = A(i) Then Return True
Next i
Return False
End Function
 
Function MinFactor(num As Integer) As Integer 'Return minimum unused factor
Dim As Integer factor, valor, min
factor = 2
min = &H7FFFFFFF
Do
If num Mod factor = 0 Then 'found a factor
valor = factor
Do
If Used(valor) Then
valor+ = factor
Else
If valor < min Then min = valor
Exit Do
End If
Loop
num \= factor
Else
factor += 1
End If
Loop Until factor > num
Return min
End Function
 
Sub EKG(m As Integer) 'Calculate and show EKG sequence
A(1) = 1: A(2) = m
For n = 3 To limite
A(n) = MinFactor(A(n - 1))
Next n
Print Using "EKG(##):"; m;
For i As Integer = 1 To limite
Print Using "###"; A(i);
Next i
Print
End Sub
 
Dim starts(4) As Integer = {2, 5, 7, 9, 10}
For i As Integer = 0 To 4
EKG(starts(i))
Next i
 
Sleep</syntaxhighlight>
{{out}}
<pre>EKG( 2): 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36
EKG( 5): 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG( 7): 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32
EKG( 9): 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG(10): 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32</pre>
 
=={{header|Go}}==
<langsyntaxhighlight lang="go">package main
 
import (
Line 234 ⟶ 720:
}
fmt.Println("\nEKG5(5) and EKG(7) do not converge within", limit, "terms")
}</langsyntaxhighlight>
 
{{out}}
Line 247 ⟶ 733:
</pre>
 
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Data.List (findIndex, isPrefixOf, tails)
import Data.Maybe (fromJust)
 
----------------------- EKG SEQUENCE ---------------------
 
seqEKGRec :: Int -> Int -> [Int] -> [Int]
seqEKGRec _ 0 l = l
seqEKGRec k n [] = seqEKGRec k (n - 2) [k, 1]
seqEKGRec k n l@(h : t) =
seqEKGRec
k
(pred n)
( head
( filter
(((&&) . flip notElem l) <*> ((1 <) . gcd h))
[2 ..]
) :
l
)
 
seqEKG :: Int -> Int -> [Int]
seqEKG k n = reverse (seqEKGRec k n [])
 
 
--------------------- CONVERGENCE TEST -------------------
main :: IO ()
main =
mapM_
( \x ->
putStr "EKG ("
>> (putStr . show $ x)
>> putStr ") is "
>> print (seqEKG x 20)
)
[2, 5, 7, 9, 10]
>> putStr "EKG(5) and EKG(7) converge at "
>> print
( succ $
fromJust $
findIndex
(isPrefixOf (replicate 20 True))
( tails
( zipWith
(==)
(seqEKG 7 80)
(seqEKG 5 80)
)
)
)</syntaxhighlight>
{{out}}
<pre>EKG (2) is [1,2,4,6,3,9,12,8,10,5,15,18,14,7,21,24,16,20,22,11]
EKG (5) is [1,5,10,2,4,6,3,9,12,8,14,7,21,15,18,16,20,22,11,33]
EKG (7) is [1,7,14,2,4,6,3,9,12,8,10,5,15,18,16,20,22,11,33,21]
EKG (9) is [1,9,3,6,2,4,8,10,5,15,12,14,7,21,18,16,20,22,11,33]
EKG (10) is [1,10,2,4,6,3,9,12,8,14,7,21,15,5,20,16,18,22,11,33]
EKG(5) and EKG(7) converge at 21</pre>
 
=={{header|J}}==
<syntaxhighlight lang="j">
Until =: 2 :'u^:(0-:v)^:_' NB. unused but so fun
prime_factors_of_tail =: ~.@:q:@:{:
numbers_not_in_list =: -.~ >:@:i.@:(>./)
 
 
ekg =: 3 :0 NB. return next sequence
if. 1 = # y do. NB. initialize
1 , y
return.
end.
a =. prime_factors_of_tail y
b =. numbers_not_in_list y
index_of_lowest =. {. _ ,~ I. 1 e."1 a e."1 q:b
if. index_of_lowest < _ do. NB. if the list doesn't need extension
y , index_of_lowest { b
return.
end.
NB. otherwise extend the list
b =. >: >./ y
while. 1 -.@:e. a e. q: b do.
b =. >: b
end.
y , b
)
 
ekg^:9&>2 5 7 9 10
1 2 4 6 3 9 12 8 10 5
1 5 10 2 4 6 3 9 12 8
1 7 14 2 4 6 3 9 12 8
1 9 3 6 2 4 8 10 5 15
1 10 2 4 6 3 9 12 8 14
 
 
assert 9 -: >:Until(>&8) 2
assert (,2) -: prime_factors_of_tail 6 8 NB. (nub of)
assert 3 4 5 -: numbers_not_in_list 1 2 6
</syntaxhighlight>
Somewhat shorter is ekg2,
<syntaxhighlight lang="j">
index_of_lowest =: [: {. _ ,~ [: I. 1 e."1 prime_factors_of_tail e."1 q:@:numbers_not_in_list
 
g =: 3 :0 NB. return sequence with next term appended
a =. prime_factors_of_tail y
(, (index_of_lowest { numbers_not_in_list)`(([: >:Until(1 e. a e. q:) [: >: >./))@.(_ = index_of_lowest)) y
)
 
ekg2 =: (1&,)`g@.(1<#)
 
assert (3 -: index_of_lowest { numbers_not_in_list)1 2 4 6
 
assert (ekg^:9&> -: ekg2^:9&>) 2 5 7 9 10
</syntaxhighlight>
 
=={{header|Java}}==
<syntaxhighlight lang="java">
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
 
public class EKGSequenceConvergence {
 
public static void main(String[] args) {
System.out.println("Calculate and show here the first 10 members of EKG[2], EKG[5], EKG[7], EKG[9] and EKG[10].");
for ( int i : new int[] {2, 5, 7, 9, 10} ) {
System.out.printf("EKG[%d] = %s%n", i, ekg(i, 10));
}
System.out.println("Calculate and show here at which term EKG[5] and EKG[7] converge.");
List<Integer> ekg5 = ekg(5, 100);
List<Integer> ekg7 = ekg(7, 100);
for ( int i = 1 ; i < ekg5.size() ; i++ ) {
if ( ekg5.get(i) == ekg7.get(i) && sameSeq(ekg5, ekg7, i)) {
System.out.printf("EKG[%d](%d) = EKG[%d](%d) = %d, and are identical from this term on%n", 5, i+1, 7, i+1, ekg5.get(i));
break;
}
}
}
// Same last element, and all elements in sequence are identical
private static boolean sameSeq(List<Integer> seq1, List<Integer> seq2, int n) {
List<Integer> list1 = new ArrayList<>(seq1.subList(0, n));
Collections.sort(list1);
List<Integer> list2 = new ArrayList<>(seq2.subList(0, n));
Collections.sort(list2);
for ( int i = 0 ; i < n ; i++ ) {
if ( list1.get(i) != list2.get(i) ) {
return false;
}
}
return true;
}
// Without HashMap to identify seen terms, need to examine list.
// Calculating 3000 terms in this manner takes 10 seconds
// With HashMap to identify the seen terms, calculating 3000 terms takes .1 sec.
private static List<Integer> ekg(int two, int maxN) {
List<Integer> result = new ArrayList<>();
result.add(1);
result.add(two);
Map<Integer,Integer> seen = new HashMap<>();
seen.put(1, 1);
seen.put(two, 1);
int minUnseen = two == 2 ? 3 : 2;
int prev = two;
for ( int n = 3 ; n <= maxN ; n++ ) {
int test = minUnseen - 1;
while ( true ) {
test++;
if ( ! seen.containsKey(test) && gcd(test, prev) > 1 ) {
result.add(test);
seen.put(test, n);
prev = test;
if ( minUnseen == test ) {
do {
minUnseen++;
} while ( seen.containsKey(minUnseen) );
}
break;
}
}
}
return result;
}
 
private static final int gcd(int a, int b) {
if ( b == 0 ) {
return a;
}
return gcd(b, a%b);
}
}
</syntaxhighlight>
{{out}}
<pre>
Calculate and show here the first 10 members of EKG[2], EKG[5], EKG[7], EKG[9] and EKG[10].
EKG[2] = [1, 2, 4, 6, 3, 9, 12, 8, 10, 5]
EKG[5] = [1, 5, 10, 2, 4, 6, 3, 9, 12, 8]
EKG[7] = [1, 7, 14, 2, 4, 6, 3, 9, 12, 8]
EKG[9] = [1, 9, 3, 6, 2, 4, 8, 10, 5, 15]
EKG[10] = [1, 10, 2, 4, 6, 3, 9, 12, 8, 14]
Calculate and show here at which term EKG[5] and EKG[7] converge.
EKG[5](21) = EKG[7](21) = 24, and are identical from this term on
</pre>
 
=={{header|jq}}==
'''Adapted from [[#Wren|Wren]]'''
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
 
A very small point of interest is that the appropriate width for printing
the results neatly is determined dynamically based on the entire set of
sequences.
 
'''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 ;
 
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
 
</syntaxhighlight>
'''The Task'''
<syntaxhighlight lang="jq">
def areSame($s; $t):
($s|length) == ($t|length) and ($s|sort) == ($t|sort);
 
def task:
 
# compare EKG5 and EKG7 for convergence, assuming . has been constructed appropriately:
def compare:
first( range(2; .limit) as $i
| select(.ekg[1][$i] == .ekg[2][$i] and areSame(.ekg[1][0:$i]; .ekg[2][0:$i]))
| "\nEKG(5) and EKG(7) converge at term \($i+1)." )
// "\nEKG5(5) and EKG(7) do not converge within \(.limit) terms." ;
 
{ limit: 100,
starts: [2, 5, 7, 9, 10],
ekg: [],
width: 0 # keep track of the number of characters required to print the results neatly
}
| reduce range(0;4) as $i (.; .ekg[$i] = [range(0; .limit) | 0] )
| reduce range(0; .starts|length ) as $s (.;
.starts[$s] as $start
| .ekg[$s][0] = 1
| .ekg[$s][1] = $start
| reduce range( 2; .limit) as $n (.;
.i = 2
| .stop = false
| until( .stop;
# a potential sequence member cannot already have been used
# and must have a factor in common with previous member
.ekg[$s] as $ekg
| if (.i | IN( $ekg[0:$n][]) | not) and gcd($ekg[$n-1]; .i) > 1
then .ekg[$s][$n] = .i
| .width = ([.width, (.i|tostring|length)] | max)
| .stop = true
else .
end
| .i += 1) ) )
 
# Read out the results of interest:
| (range(0; .starts|length ) as $s
| .width as $width
| "EKG(\(.starts[$s]|lpad(2))): \(.ekg[$s][0:30]|map(lpad($width))|join(" "))" ),
compare
;
 
task</syntaxhighlight>
{{out}}
<pre>
EKG( 2): 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36
EKG( 5): 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG( 7): 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32
EKG( 9): 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG(10): 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32
 
EKG(5) and EKG(7) converge at term 21.
</pre>
 
=={{header|Julia}}==
{{trans|Perl}}
<langsyntaxhighlight lang="julia">using Primes
 
function ekgsequence(n, limit)
Line 278 ⟶ 1,048:
[println(rpad("EKG($i): ", 9), join(ekgsequence(i, 30), " ")) for i in [2, 5, 7, 9, 10]]
println("EKGs of 5 & 7 converge at term ", convergeat(5, 7))
</syntaxhighlight>
</lang>
{{output}}<pre>
EKG(2): 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36
Line 290 ⟶ 1,060:
=={{header|Kotlin}}==
{{trans|Go}}
<langsyntaxhighlight lang="scala">// Version 1.2.60
 
fun gcd(a: Int, b: Int): Int {
Line 338 ⟶ 1,108:
}
println("\nEKG5(5) and EKG(7) do not converge within $LIMIT terms")
}</langsyntaxhighlight>
 
{{output}}
Line 350 ⟶ 1,120:
EKG(5) and EKG(7) converge at term 21
</pre>
 
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[NextInSequence, EKGSequence]
NextInSequence[seq_List] := Module[{last, new = 1, holes, max, sel, found, i},
last = Last[seq];
max = Max[seq];
holes = Complement[Range[max], seq];
sel = SelectFirst[holes, Not[CoprimeQ[last, #]] &];
If[MissingQ[sel],
i = max;
found = False;
While[! found,
i++;
If[Not[CoprimeQ[last, i]],
found = True
]
];
Append[seq, i]
,
Append[seq, sel]
]
]
EKGSequence[start_Integer, n_] := Nest[NextInSequence, {1, start}, n - 2]
 
Table[EKGSequence[s, 10], {s, {2, 5, 7, 9, 10}}] // Grid
 
s = Reverse[Transpose[{EKGSequence[5, 1000], EKGSequence[7, 1000]}]];
len = LengthWhile[s, Apply[Equal]];
s //= Reverse[Drop[#, len]] &;
Length[s] + 1</syntaxhighlight>
{{out}}
<pre>1 2 4 6 3 9 12 8 10 5
1 5 10 2 4 6 3 9 12 8
1 7 14 2 4 6 3 9 12 8
1 9 3 6 2 4 8 10 5 15
1 10 2 4 6 3 9 12 8 14
 
21</pre>
 
=={{header|MATLAB}}==
{{trans|Julia}}
<syntaxhighlight lang="MATLAB">
% Displaying EKG sequences and the convergence point
for i = [2, 5, 7, 9, 10]
ekg = ekgsequence(i, 30);
fprintf('EKG(%d): %s\n', i, num2str(ekg));
end
 
convergencePoint = convergeat(5, 7);
fprintf('EKGs of 5 & 7 converge at term %d\n', convergencePoint);
 
 
 
function ekg = ekgsequence(n, limit)
ekg = [1, n];
while length(ekg) < limit
for i = 2:2^18
if all(ekg ~= i) && gcd(ekg(end), i) > 1
ekg = [ekg, i];
break;
end
end
end
end
 
function point = convergeat(n, m, max)
if nargin < 3
max = 100;
end
 
ekgn = ekgsequence(n, max);
ekgm = ekgsequence(m, max);
point = 0;
for i = 3:max
if ekgn(i) == ekgm(i) && sum(ekgn(1:i+1)) == sum(ekgm(1:i+1))
point = i;
return;
end
end
if point == 0
warning('No convergence in %d terms', max);
end
end
</syntaxhighlight>
{{out}}
<pre>
EKG(2): 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36
EKG(5): 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG(7): 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32
EKG(9): 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG(10): 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32
EKGs of 5 & 7 converge at term 21
</pre>
 
 
=={{header|Nim}}==
<syntaxhighlight lang="nim">import algorithm, math, sets, strformat, strutils
 
#---------------------------------------------------------------------------------------------------
 
iterator ekg(n, limit: Positive): (int, int) =
var values: HashSet[int]
doAssert n >= 2
yield (1, 1)
yield (2, n)
values.incl(n)
var i = 3
var prev = n
while i <= limit:
var val = 2
while true:
if val notin values and gcd(val, prev) != 1:
values.incl(val)
yield (i, val)
prev = val
break
inc val
inc i
 
#---------------------------------------------------------------------------------------------------
 
for n in [2, 5, 7, 9, 10]:
var result: array[1..10, int]
for i, val in ekg(n, 10): result[i] = val
let title = fmt"EKG({n}):"
echo fmt"{title:8} {result.join("", "")}"
 
var ekg5, ekg7: array[1..100, int]
for i, val in ekg(5, 100): ekg5[i] = val
for i, val in ekg(7, 100): ekg7[i] = val
var convIndex = 0
for i in 2..100:
if ekg5[i] == ekg7[i] and sorted(ekg5[1..<i]) == sorted(ekg7[1..<i]):
convIndex = i
break
if convIndex > 0:
echo fmt"EKG(5) and EKG(7) converge at index {convIndex}."
else:
echo "No convergence found in the first {convIndex} terms."</syntaxhighlight>
 
{{out}}
<pre>EKG(2): 1, 2, 4, 6, 3, 9, 12, 8, 10, 5
EKG(5): 1, 5, 10, 2, 4, 6, 3, 9, 12, 8
EKG(7): 1, 7, 14, 2, 4, 6, 3, 9, 12, 8
EKG(9): 1, 9, 3, 6, 2, 4, 8, 10, 5, 15
EKG(10): 1, 10, 2, 4, 6, 3, 9, 12, 8, 14
EKG(5) and EKG(7) converge at index 21.</pre>
 
=={{header|Perl}}==
{{trans|Perl 6Raku}}
<langsyntaxhighlight lang="perl">use List::Util qw(none sum);
 
sub gcd { my ($u,$v) = @_; $v ? gcd($v, $u%$v) : abs($u) }
Line 380 ⟶ 1,299:
 
print "EKG($_): " . join(' ', EKG($_,10)) . "\n" for 2, 5, 7, 9, 10;
print "EKGs of 5 & 7 converge at term " . converge_at(5, 7) . "\n"</langsyntaxhighlight>
{{out}}
<pre>EKG(2): 1 2 4 6 3 9 12 8 10 5
Line 388 ⟶ 1,307:
EKG(10): 1 10 2 4 6 3 9 12 8 14
EKGs of 5 & 7 converge at term 21</pre>
 
=={{header|Perl 6}}==
{{works with|Rakudo Star|2018.04.1}}
<lang perl6>sub infix:<shares-divisors-with> { ($^a gcd $^b) > 1 }
 
sub next-EKG ( *@s ) {
return first {
@s ∌ $_ and @s.tail shares-divisors-with $_
}, 2..*;
}
 
sub EKG ( Int $start ) { 1, $start, &next-EKG … * }
 
sub converge-at ( @ints ) {
my @ekgs = @ints.map: &EKG;
 
return (2 .. *).first: -> $i {
[==] @ekgs.map( *.[$i] ) and
[===] @ekgs.map( *.head($i).Set )
}
}
 
say "EKG($_): ", .&EKG.head(10) for 2, 5, 7, 9, 10;
 
for [5, 7], [2, 5, 7, 9, 10] -> @ints {
say "EKGs of (@ints[]) converge at term {$_+1}" with converge-at(@ints);
}</lang>
{{out}}
<pre>
EKG(2): (1 2 4 6 3 9 12 8 10 5)
EKG(5): (1 5 10 2 4 6 3 9 12 8)
EKG(7): (1 7 14 2 4 6 3 9 12 8)
EKG(9): (1 9 3 6 2 4 8 10 5 15)
EKG(10): (1 10 2 4 6 3 9 12 8 14)
EKGs of (5 7) converge at term 21
EKGs of (2 5 7 9 10) converge at term 45
</pre>
 
=={{header|Phix}}==
{{trans|C}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>constant LIMIT = 100
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
constant starts = {2, 5, 7, 9, 10}
<span style="color: #008080;">constant</span> <span style="color: #000000;">LIMIT</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span>
sequence ekg = {}
<span style="color: #008080;">constant</span> <span style="color: #000000;">starts</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">}</span>
string fmt = "EKG(%2d): ["&join(repeat("%d",min(LIMIT,30))," ")&"]\n"
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ekg</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
for s=1 to length(starts) do
<span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"EKG(%2d): ["</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">LIMIT</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)),</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"]\n"</span>
ekg = append(ekg,{1,starts[s]}&repeat(0,LIMIT-2))
<span style="color: #008080;">for</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">starts</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
for n=3 to LIMIT do
<span style="color: #000000;">ekg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">starts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">LIMIT</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))</span>
-- a potential sequence member cannot already have been used
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">LIMIT</span> <span style="color: #008080;">do</span>
-- and must have a factor in common with previous member
<span style="color: #000080;font-style:italic;">-- a potential sequence member cannot already have been used
integer i = 2
-- and must have a factor in common with previous member</span>
while find(i,ekg[s])
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
or gcd(ekg[s][n-1],i)<=1 do
<span style="color: #008080;">while</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">])</span>
i += 1
<span style="color: #008080;">or</span> <span style="color: #7060A8;">gcd</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)<=</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
end while
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
ekg[s][n] = i
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
end for
<span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">][</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span>
printf(1,fmt,starts[s]&ekg[s][1..min(LIMIT,30)])
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end for
<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: #000000;">fmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">starts</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]&</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">LIMIT</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">)])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
-- now compare EKG5 and EKG7 for convergence
constant EKG5 = find(5,starts),
<span style="color: #000080;font-style:italic;">-- now compare EKG5 and EKG7 for convergence</span>
EKG7 = find(7,starts)
<span style="color: #008080;">constant</span> <span style="color: #000000;">EKG5</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">starts</span><span style="color: #0000FF;">),</span>
string msg = sprintf("do not converge within %d terms", LIMIT)
<span style="color: #000000;">EKG7</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">starts</span><span style="color: #0000FF;">)</span>
for i=3 to LIMIT do
<span style="color: #004080;">string</span> <span style="color: #000000;">msg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"do not converge within %d terms"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">LIMIT</span><span style="color: #0000FF;">)</span>
if ekg[EKG5][i]=ekg[EKG7][i]
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">LIMIT</span> <span style="color: #008080;">do</span>
and sort(ekg[EKG5][1..i-1])=sort(ekg[EKG7][1..i-1]) then
<span style="color: #008080;">if</span> <span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">EKG5</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">EKG7</span><span style="color: #0000FF;">][</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
msg = sprintf("converge at term %d", i)
<span style="color: #008080;">and</span> <span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">EKG5</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])=</span><span style="color: #7060A8;">sort</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ekg</span><span style="color: #0000FF;">[</span><span style="color: #000000;">EKG7</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">then</span>
exit
<span style="color: #000000;">msg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"converge at term %d"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #008080;">exit</span>
end for
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
printf(1,"\nEKG5(5) and EKG(7) %s\n", msg)</lang>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"\nEKG5(5) and EKG(7) %s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">msg</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 474 ⟶ 1,359:
If this alternate definition of function EKG_gen is used then the output would be the same as above.
Instead of keeping a cache of prime factors this calculates the gretest common divisor as needed.
<langsyntaxhighlight lang="python">from itertools import count, islice, takewhile
from math import gcd
 
Line 507 ⟶ 1,392:
for start in 2, 5, 7, 9, 10:
print(f"EKG({start}):", str([n[0] for n in islice(EKG_gen(start), 10)])[1: -1])
print(f"\nEKG(5) and EKG(7) converge at term {find_convergence(ekgs=(5,7))}!")</langsyntaxhighlight>
 
{{out}}
Line 522 ⟶ 1,407:
Despite EKG(5) and EKG(7) seeming to converge earlier, as seen above; their hidden states differ.<br>
Here is those series out to 21 terms where you can see them diverge again before finally converging. The state is also shown.
<langsyntaxhighlight lang="python"># After running the above, in the terminal:
from pprint import pprint as pp
 
for start in 5, 7:
print(f"EKG({start}):\n[(<next>, [<state>]), ...]")
pp(([n for n in islice(EKG_gen(start), 21)]))</langsyntaxhighlight>
 
'''Generates:'''
Line 576 ⟶ 1,461:
(21, [13, 17, 19, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]),
(24, [13, 17, 19, 23, 25, 26, 27, 28, 29, 30, 31, 32])]</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo Star|2018.04.1}}
<syntaxhighlight lang="raku" line>sub infix:<shares-divisors-with> { ($^a gcd $^b) > 1 }
 
sub next-EKG ( *@s ) {
return first {
@s ∌ $_ and @s.tail shares-divisors-with $_
}, 2..*;
}
 
sub EKG ( Int $start ) { 1, $start, &next-EKG … * }
 
sub converge-at ( @ints ) {
my @ekgs = @ints.map: &EKG;
 
return (2 .. *).first: -> $i {
[==] @ekgs.map( *.[$i] ) and
[===] @ekgs.map( *.head($i).Set )
}
}
 
say "EKG($_): ", .&EKG.head(10) for 2, 5, 7, 9, 10;
 
for [5, 7], [2, 5, 7, 9, 10] -> @ints {
say "EKGs of (@ints[]) converge at term {$_+1}" with converge-at(@ints);
}</syntaxhighlight>
{{out}}
<pre>
EKG(2): (1 2 4 6 3 9 12 8 10 5)
EKG(5): (1 5 10 2 4 6 3 9 12 8)
EKG(7): (1 7 14 2 4 6 3 9 12 8)
EKG(9): (1 9 3 6 2 4 8 10 5 15)
EKG(10): (1 10 2 4 6 3 9 12 8 14)
EKGs of (5 7) converge at term 21
EKGs of (2 5 7 9 10) converge at term 45
</pre>
 
=={{header|REXX}}==
<langsyntaxhighlight lang="rexx">/*REXX program can generate and display several EKG sequences (with various starts).*/
parse arg nums start /*obtain optional arguments from the CL*/
if nums=='' | nums=="," then nums= 50 /*Not specified? Then use the default.*/
Line 616 ⟶ 1,539:
if done then iterate
if wordpos(j, $)==0 then return j /*return an EKG integer.*/
end /*j*/</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<!-- (output is shown &nbsp; '''<sup>5</sup>/<sub>6</sub>''' &nbsp; size.) !-->
Line 629 ⟶ 1,552:
 
(start 10): 1 10 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32 34 17 51 36 38 19 57 42 40 44 46 23 69 45 48 50 52 54 56 49 63
</pre>
 
=={{header|Rust}}==
{{trans|Perl}}
<syntaxhighlight lang="rust">use gcd::Gcd;
 
fn ekg_sequence(n: u64, limit: usize) -> Vec<u64> {
let mut ekg = [1_u64, n].to_vec();
while ekg.len() < limit {
for i in 2..2<<18 {
if ekg.iter().all(|j| *j != i) && Gcd::gcd(ekg[ekg.len()-1], i) > 1 {
ekg.push(i);
break;
}
}
}
return ekg;
}
 
 
fn converge_at(n: u64, m: u64, tmax: usize) -> usize {
let a = ekg_sequence(n, tmax);
let b = ekg_sequence(m, tmax);
for i in 2..tmax {
if a[i] == b[i] && a[0..i+1].iter().sum::<u64>() == (b[0..i+1]).iter().sum::<u64>() {
return i + 1;
}
}
println!("Error: no convergence in {tmax} terms");
return 0;
}
 
fn main() {
for i in [2_u64, 5, 7, 9, 10] {
println!("EKG({i:2}): {:?}", ekg_sequence(i, 30_usize));
}
println!("EKGs of 5 & 7 converge after term {:?}", converge_at(5, 7, 50));
}
</syntaxhighlight>{{out}}
<pre style="font-size:90%">
EKG( 2): [1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 14, 7, 21, 24, 16, 20, 22, 11, 33, 27, 30, 25, 35, 28, 26, 13, 39, 36]
EKG( 5): [1, 5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKG( 7): [1, 7, 14, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 16, 20, 22, 11, 33, 21, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKG( 9): [1, 9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKG(10): [1, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 5, 20, 16, 18, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKGs of 5 & 7 converge after term 21
</pre>
 
=={{header|Sidef}}==
{{trans|Raku}}
<syntaxhighlight lang="ruby">class Seq(terms, callback) {
method next {
terms += callback(terms)
}
 
method nth(n) {
while (terms.len < n) {
self.next
}
terms[n-1]
}
 
method first(n) {
while (terms.len < n) {
self.next
}
terms.first(n)
}
}
 
func next_EKG (s) {
2..Inf -> first {|k|
!(s.contains(k) || s[-1].is_coprime(k))
}
}
 
func EKG (start) {
Seq([1, start], next_EKG)
}
 
func converge_at(ints) {
var ekgs = ints.map(EKG)
 
2..Inf -> first {|k|
(ekgs.map { .nth(k) }.uniq.len == 1) &&
(ekgs.map { .first(k).sort }.uniq.len == 1)
}
}
 
for k in [2, 5, 7, 9, 10] {
say "EKG(#{k}) = #{EKG(k).first(10)}"
}
 
for arr in [[5,7], [2, 5, 7, 9, 10]] {
var c = converge_at(arr)
say "EKGs of #{arr} converge at term #{c}"
}</syntaxhighlight>
{{out}}
<pre>
EKG(2) = [1, 2, 4, 6, 3, 9, 12, 8, 10, 5]
EKG(5) = [1, 5, 10, 2, 4, 6, 3, 9, 12, 8]
EKG(7) = [1, 7, 14, 2, 4, 6, 3, 9, 12, 8]
EKG(9) = [1, 9, 3, 6, 2, 4, 8, 10, 5, 15]
EKG(10) = [1, 10, 2, 4, 6, 3, 9, 12, 8, 14]
EKGs of [5, 7] converge at term 21
EKGs of [2, 5, 7, 9, 10] converge at term 45
</pre>
 
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="v (vlang)">fn gcd(aa int, bb int) int {
mut a,mut b:=aa,bb
for a != b {
if a > b {
a -= b
} else {
b -= a
}
}
return a
}
fn are_same(ss []int, tt []int) bool {
mut s,mut t:=ss.clone(),tt.clone()
le := s.len
if le != t.len {
return false
}
s.sort()
t.sort()
for i in 0..le {
if s[i] != t[i] {
return false
}
}
return true
}
const limit = 100
fn main() {
starts := [2, 5, 7, 9, 10]
mut ekg := [5][limit]int{}
for s, start in starts {
ekg[s][0] = 1
ekg[s][1] = start
for n in 2..limit {
for i := 2; ; i++ {
// a potential sequence member cannot already have been used
// and must have a factor in common with previous member
if !ekg[s][..n].contains(i) && gcd(ekg[s][n-1], i) > 1 {
ekg[s][n] = i
break
}
}
}
println("EKG(${start:2}): ${ekg[s][..30]}")
}
// now compare EKG5 and EKG7 for convergence
for i in 2..limit {
if ekg[1][i] == ekg[2][i] && are_same(ekg[1][..i], ekg[2][..i]) {
println("\nEKG(5) and EKG(7) converge at term ${i+1}")
return
}
}
println("\nEKG5(5) and EKG(7) do not converge within $limit terms")
}</syntaxhighlight>
 
{{out}}
<pre>
EKG( 2): [1, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 14, 7, 21, 24, 16, 20, 22, 11, 33, 27, 30, 25, 35, 28, 26, 13, 39, 36]
EKG( 5): [1, 5, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 18, 16, 20, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKG( 7): [1, 7, 14, 2, 4, 6, 3, 9, 12, 8, 10, 5, 15, 18, 16, 20, 22, 11, 33, 21, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKG( 9): [1, 9, 3, 6, 2, 4, 8, 10, 5, 15, 12, 14, 7, 21, 18, 16, 20, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
EKG(10): [1, 10, 2, 4, 6, 3, 9, 12, 8, 14, 7, 21, 15, 5, 20, 16, 18, 22, 11, 33, 24, 26, 13, 39, 27, 30, 25, 35, 28, 32]
 
EKG(5) and EKG(7) converge at term 21
</pre>
 
=={{header|Wren}}==
{{trans|Go}}
{{libheader|Wren-sort}}
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./sort" for Sort
import "./math" for Int
import "./fmt" for Fmt
 
var areSame = Fn.new { |s, t|
var le = s.count
if (le != t.count) return false
Sort.quick(s)
Sort.quick(t)
for (i in 0...le) if (s[i] != t[i]) return false
return true
}
 
var limit = 100
var starts = [2, 5, 7, 9, 10]
var ekg = List.filled(5, null)
for (i in 0..4) ekg[i] = List.filled(limit, 0)
var s = 0
for (start in starts) {
ekg[s][0] = 1
ekg[s][1] = start
for (n in 2...limit) {
var i = 2
while (true) {
// a potential sequence member cannot already have been used
// and must have a factor in common with previous member
if (!ekg[s].take(n).contains(i) && Int.gcd(ekg[s][n-1], i) > 1) {
ekg[s][n] = i
break
}
i = i + 1
}
}
Fmt.print("EKG($2d): $2d", start, ekg[s].take(30).toList)
s = s + 1
}
 
// now compare EKG5 and EKG7 for convergence
for (i in 2...limit) {
if (ekg[1][i] == ekg[2][i] && areSame.call(ekg[1][0...i], ekg[2][0...i])) {
System.print("\nEKG(5) and EKG(7) converge at term %(i+1).")
return
}
}
System.print("\nEKG5(5) and EKG(7) do not converge within %(limit) terms.") </syntaxhighlight>
 
{{out}}
<pre>
EKG( 2): 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36
EKG( 5): 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG( 7): 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32
EKG( 9): 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG(10): 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32
 
EKG(5) and EKG(7) converge at term 21.
</pre>
 
=={{header|XPL0}}==
As can be seen, EKG(5) and EKG(7) converge at N = 21.
<syntaxhighlight lang="xpl0">int N, A(1+30);
 
func Used; int M; \Return 'true' if M is in array A
int I;
[for I:= 1 to N-1 do
if M = A(I) then return true;
return false;
];
 
func MinFactor; int Num; \Return minimum unused factor
int Fac, Val, Min;
[Fac:= 2;
Min:= -1>>1;
repeat if rem(Num/Fac) = 0 then \found a factor
[Val:= Fac;
loop [if Used(Val) then Val:= Val+Fac
else [if Val<Min then Min:= Val;
quit;
];
];
Num:= Num/Fac;
]
else Fac:= Fac+1;
until Fac > Num;
return Min;
];
 
proc EKG; int M; \Calculate and show EKG sequence
[A(1):= 1; A(2):= M;
for N:= 3 to 30 do
A(N):= MinFactor(A(N-1));
Format(2, 0);
Text(0, "EKG("); RlOut(0, float(M)); Text(0, "):");
Format(3, 0);
for N:= 1 to 30 do
RlOut(0, float(A(N)));
CrLf(0);
];
 
int Tbl, I;
[Tbl:= [2, 5, 7, 9, 10];
for I:= 0 to 4 do EKG(Tbl(I));
]</syntaxhighlight>
 
{{out}}
<pre>
EKG( 2): 1 2 4 6 3 9 12 8 10 5 15 18 14 7 21 24 16 20 22 11 33 27 30 25 35 28 26 13 39 36
EKG( 5): 1 5 10 2 4 6 3 9 12 8 14 7 21 15 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG( 7): 1 7 14 2 4 6 3 9 12 8 10 5 15 18 16 20 22 11 33 21 24 26 13 39 27 30 25 35 28 32
EKG( 9): 1 9 3 6 2 4 8 10 5 15 12 14 7 21 18 16 20 22 11 33 24 26 13 39 27 30 25 35 28 32
EKG(10): 1 10 2 4 6 3 9 12 8 14 7 21 15 5 20 16 18 22 11 33 24 26 13 39 27 30 25 35 28 32
</pre>
 
=={{header|zkl}}==
Using gcd hint from Go.
<langsyntaxhighlight lang="zkl">fcn ekgW(N){ // --> iterator
Walker.tweak(fcn(rp,buf,w){
foreach n in (w){
Line 641 ⟶ 1,858:
}
}.fp(Ref(N),List(),Walker.chain([2..N-1],[N+1..]))).push(1,N)
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">foreach n in (T(2,5,7,9,10)){ println("EKG(%2d): %s".fmt(n,ekgW(n).walk(10).concat(","))) }</langsyntaxhighlight>
{{out}}
<pre>
Line 651 ⟶ 1,868:
EKG(10): 1,10,2,4,6,3,9,12,8,14
</pre>
<langsyntaxhighlight lang="zkl">fcn convergeAt(n1,n2,etc){ ns:=vm.arglist;
ekgWs:=ns.apply(ekgW); ekgWs.apply2("next"); // pop initial 1
ekgNs:=List()*vm.numArgs; // ( (ekg(n1)), (ekg(n2)) ...)
Line 666 ⟶ 1,883:
}
convergeAt(5,7);
convergeAt(2,5,7,9,10);</langsyntaxhighlight>
{{out}}
<pre>
Jjuanhdez
2,130

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