Rosetta Code

EKG sequence convergence: Difference between revisions

Page Discussion

EKG sequence convergence (view source)

Revision as of 08:23, 17 March 2024

59,341 bytes added ,  3 months ago
Added FreeBASIC
(→‎Python: Using math.gcd: Make entry a complete program to better highlight complexity difference.)
(Added FreeBASIC)
 
(79 intermediate revisions by 28 users not shown)
Line 1:
{{draft task}}
 
The sequence is from the natural numbers and is defined by:
* <code>a(1) = 1</code>;
Line 12 ⟶ 13:
* ... the sequence starting <code>1, N, ...</code> the <code>EKG(N)</code> sequence.
 
 
'''Convergence'''<br>
;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> if <code>state_of(EKG(N1).a(c)) == state_of(EKG(N2).a(c))</code>.
 
;Task:
 
;Task:
# Calculate and show here the first ten members of <code>EKG(2)</code>.
# Calculate and show here the first ten10 members of <code>EKG(52)</code>.
# Calculate and show here the first ten10 members of <code>EKG(75)</code>.
# '''Stretch goal''': Calculate and show here atthe whichfirst term10 EKG(5)members andof <code>EKG(7) converge</code>.
# Calculate and show here the first 10 members of <code>EKG(9)</code>.
# 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''').
 
;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}}
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdlib.h>
 
#define TRUE 1
#define FALSE 0
#define LIMIT 100
 
typedef int bool;
 
int compareInts(const void *a, const void *b) {
int aa = *(int *)a;
int bb = *(int *)b;
return aa - bb;
}
 
bool contains(int a[], int b, size_t len) {
int i;
for (i = 0; i < len; ++i) {
if (a[i] == b) return TRUE;
}
return FALSE;
}
 
int gcd(int a, int b) {
while (a != b) {
if (a > b)
a -= b;
else
b -= a;
}
return a;
}
 
bool areSame(int s[], int t[], size_t len) {
int i;
qsort(s, len, sizeof(int), compareInts);
qsort(t, len, sizeof(int), compareInts);
for (i = 0; i < len; ++i) {
if (s[i] != t[i]) return FALSE;
}
return TRUE;
}
 
int main() {
int s, n, i;
int starts[5] = {2, 5, 7, 9, 10};
int ekg[5][LIMIT];
for (s = 0; s < 5; ++s) {
ekg[s][0] = 1;
ekg[s][1] = starts[s];
for (n = 2; n < LIMIT; ++n) {
for (i = 2; ; ++i) {
// a potential sequence member cannot already have been used
// and must have a factor in common with previous member
if (!contains(ekg[s], i, n) && gcd(ekg[s][n - 1], i) > 1) {
ekg[s][n] = i;
break;
}
}
}
printf("EKG(%2d): [", starts[s]);
for (i = 0; i < 30; ++i) printf("%d ", ekg[s][i]);
printf("\b]\n");
}
// now compare EKG5 and EKG7 for convergence
for (i = 2; i < LIMIT; ++i) {
if (ekg[1][i] == ekg[2][i] && areSame(ekg[1], ekg[2], i)) {
printf("\nEKG(5) and EKG(7) converge at term %d\n", i + 1);
return 0;
}
}
printf("\nEKG5(5) and EKG(7) do not converge within %d terms\n", LIMIT);
return 0;
}</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++}}==
<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>
 
=={{header|F_Sharp|F#}}==
===The Function===
This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_function Extensible Prime Generator (F#)]
<syntaxhighlight lang="fsharp">
// Generate EKG Sequences. Nigel Galloway: December 6th., 2018
let EKG n=seq{
let fN,fG=let i=System.Collections.Generic.Dictionary<int,int>()
let fN g=(if not (i.ContainsKey g) then i.[g]<-g);(g,i.[g])
((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 (α,β)=seq{let b=fU β in if (β=n||β<snd((fG b|>List.maxBy snd))) then fN α; yield! EKG l (fG l|>List.minBy snd)
else fN α;yield β;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)
</syntaxhighlight>
 
===The Task===
<syntaxhighlight lang="fsharp">
EKG 2 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
EKG 3 |> Seq.take 45 |> Seq.iter(printf "%2d, ")
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>
{{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===
<syntaxhighlight lang="fsharp">
prıntfn "%d" (EKG 2|>Seq.takeWhile(fun n->n<>104729) ((Seq.length n)+1)
</syntaxhighlight>
{{out}}
<pre>
203786
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 71 ⟶ 693:
func main() {
const limit = 100
starts := [35]int{2, 5, 7, 9, 10}
var ekg [35][limit]int
 
for s, start := range starts {
ekg[s][0] = 1
ekg[s][1] = start
nextMember:
for n := 2; n < limit; n++ {
for i := 2; ; i++ {
Line 84 ⟶ 705:
if !contains(ekg[s][:n], i) && gcd(ekg[s][n-1], i) > 1 {
ekg[s][n] = i
continue nextMemberbreak
}
}
}
fmt.Printf("EKG(%d2d): %v\n", start, ekg[s][:1030])
}
 
// now compare EKG5 and EKG7 for convergence
for i := 12; i < limit; i++ {
if ekg[1][i] == ekg[2][i] && areSame(ekg[1][:i], ekg[2][:i]) {
fmt.Println("\nEKG(5) and EKG(7) converge at term", i+1)
Line 99 ⟶ 720:
}
fmt.Println("\nEKG5(5) and EKG(7) do not converge within", limit, "terms")
}</langsyntaxhighlight>
 
{{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|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}}
<syntaxhighlight lang="julia">using Primes
 
function ekgsequence(n, limit)
ekg::Array{Int,1} = [1, n]
while length(ekg) < limit
for i in 2:2<<18
if all(j -> j != i, ekg) && gcd(ekg[end], i) > 1
push!(ekg, i)
break
end
end
end
ekg
end
 
function convergeat(n, m, max = 100)
ekgn = ekgsequence(n, max)
ekgm = ekgsequence(m, max)
for i in 3:max
if ekgn[i] == ekgm[i] && sum(ekgn[1:i+1]) == sum(ekgm[1:i+1])
return i
end
end
warn("no converge in $max terms")
end
 
[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>
{{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
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|Kotlin}}==
{{trans|Go}}
<langsyntaxhighlight lang="scala">// Version 1.2.60
 
fun gcd(a: Int, b: Int): Int {
Line 129 ⟶ 1,077:
 
fun main(args: Array<String>) {
val starts = listOf(2, 5, 7, 9, 10)
val ekg = Array(35) { IntArray(LIMIT) }
 
for ((s, start) in starts.withIndex()) {
ekg[s][0] = 1
ekg[s][1] = start
nextMember@ for (n in 2 until LIMIT) {
var i = 2
while (true) {
Line 143 ⟶ 1,091:
gcd(ekg[s][n - 1], i) > 1) {
ekg[s][n] = i
continue@nextMemberbreak
}
i++
}
}
System.out.printf("EKG(%d2d): %s\n", start, ekg[s].slice(0 until 1030))
}
 
// now compare EKG5 and EKG7 for convergence
for (i in 12 until LIMIT) {
if (ekg[1][i] == ekg[2][i] &&
ekg[1].slice(0 until i).sorted() == ekg[2].slice(0 until i).sorted()) {
Line 160 ⟶ 1,108:
}
println("\nEKG5(5) and EKG(7) do not converge within $LIMIT terms")
}</langsyntaxhighlight>
 
{{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]
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|PythonMathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[NextInSequence, EKGSequence]
===Python: Using prime factor generation===
NextInSequence[seq_List] := Module[{last, new = 1, holes, max, sel, found, i},
<lang python>from itertools import count, islice, takewhile
last = Last[seq];
from functools import lru_cache
max = Max[seq];
holes = Complement[Range[max], seq];
primes = [2, 3, 5, 7, 11, 13, 17] # Will be extended
sel = SelectFirst[holes, Not[CoprimeQ[last, #]] &];
If[MissingQ[sel],
@lru_cache(maxsize=2000)
i = max;
def pfactor(n):
found = False;
# From; http://rosettacode.org/wiki/Count_in_factors
While[! found,
if n == 1:
return [1]i++;
If[Not[CoprimeQ[last, i]],
n2 = n // 2 + 1
for pfound in= primes:True
if p <= n2:]
];
d, m = divmod(n, p)
Append[seq, i]
if m == 0:
,
if d > 1:
Append[seq, sel]
return [p] + pfactor(d)
]
else:
]
return [p]
EKGSequence[start_Integer, n_] := Nest[NextInSequence, {1, start}, n - 2]
else:
if n > primes[-1]:
primes.append(n)
return [n]
 
Table[EKGSequence[s, 10], {s, {2, 5, 7, 9, 10}}] // Grid
def next_pfactor_gen():
"Generate (n, set(pfactor(n))) pairs for n == 2, ..."
for n in count(2):
yield n, set(pfactor(n))
 
s = Reverse[Transpose[{EKGSequence[5, 1000], EKGSequence[7, 1000]}]];
def EKG_gen(start=2):
len = LengthWhile[s, Apply[Equal]];
"""\
s //= Reverse[Drop[#, len]] &;
Generate the next term of the EKG together with the minimum cache of
Length[s] + 1</syntaxhighlight>
numbers left in its production; (the "state" of the generator).
{{out}}
"""
<pre>1 2 4 6 3 9 12 8 10 5
def min_share_pf_so_far(pf, so_far):
1 5 10 2 4 6 3 9 12 8
"searches the unused smaller number prime factors"
1 7 14 2 4 6 3 9 12 8
nonlocal found
1 9 3 6 2 4 8 10 5 15
for index, (num, pfs) in enumerate(so_far):
1 10 2 4 6 3 9 12 8 14
if pf & pfs:
found = so_far.pop(index)
break
else:
found = ()
return found
 
21</pre>
yield 1, []
last, last_pf = start, set(pfactor(start))
pf_gen = next_pfactor_gen()
# minimum list of prime factors needed so far
so_far = list(islice(pf_gen, start))
found = ()
while True:
while not min_share_pf_so_far(last_pf, so_far):
so_far.append(next(pf_gen))
yield found[0], [n for n, _ in so_far]
last, last_pf = found
#%%
def find_convergence(ekgs=(5,7), limit=1_000):
"Returns the convergence point or zero if not found within the limit"
ekg = [EKG_gen(n) for n in ekgs]
for e in ekg:
next(e) # skip initial 1 in each sequence
differ = list(takewhile(lambda state: not all(state[0] == s for s in state[1:]),
islice(zip(*ekg), limit-1)))
ldiff = len(differ)
return ldiff + 2 if ldiff < limit-1 else 0
 
=={{header|MATLAB}}==
#%%
{{trans|Julia}}
if __name__ == '__main__':
<syntaxhighlight lang="MATLAB">
for start in 2, 5, 7:
% Displaying EKG sequences and the convergence point
print(f"EKG({start}):", str([n[0] for n in islice(EKG_gen(start), 10)])[1: -1])
for i = [2, 5, 7, 9, 10]
print(f"\nEKG(5) and EKG(7) converge at term {find_convergence(ekgs=(5,7))}!")</lang>
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>
<pre>EKG(2): 1, 2, 4, 6, 3, 9, 12, 8, 10, 5
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
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
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>
 
EKG(5) and EKG(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|Raku}}
<syntaxhighlight lang="perl">use List::Util qw(none sum);
 
sub gcd { my ($u,$v) = @_; $v ? gcd($v, $u%$v) : abs($u) }
sub shares_divisors_with { gcd( $_[0], $_[1]) > 1 }
 
sub EKG {
my($n,$limit) = @_;
my @ekg = (1, $n);
while (@ekg < $limit) {
for my $i (2..1e18) {
next unless none { $_ == $i } @ekg and shares_divisors_with($ekg[-1], $i);
push(@ekg, $i) and last;
}
}
@ekg;
}
 
sub converge_at {
my($n1,$n2) = @_;
my $max = 100;
my @ekg1 = EKG($n1,$max);
my @ekg2 = EKG($n2,$max);
do { return $_+1 if $ekg1[$_] == $ekg2[$_] && sum(@ekg1[0..$_]) == sum(@ekg2[0..$_])} for 2..$max;
return "(no convergence in $max terms)";
}
 
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"</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</pre>
 
=={{header|Phix}}==
{{trans|C}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">LIMIT</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">100</span>
<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>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ekg</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<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>
<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>
<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>
<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>
<span style="color: #000080;font-style:italic;">-- a potential sequence member cannot already have been used
-- and must have a factor in common with previous member</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
<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>
<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>
<span style="color: #000000;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</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: #0000FF;">=</span> <span style="color: #000000;">i</span>
<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: #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>
<span style="color: #000080;font-style:italic;">-- now compare EKG5 and EKG7 for convergence</span>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<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>
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]
 
EKG5(5) and EKG(7) converge at term 21
</pre>
 
=={{header|Python}}==
===Python: Using math.gcd===
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 273 ⟶ 1,376:
if gcd(last, sf) > 1:
last = so_far.pop(index)
yield last, so_far[::]
break
else:
Line 287 ⟶ 1,390:
 
if __name__ == '__main__':
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}}
(Output is the sameSame as above).
<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 term 21!</pre>
 
;Note:
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.
<syntaxhighlight 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)]))</syntaxhighlight>
 
'''Generates:'''
<pre>EKG(5):
[(<next>, [<state>]), ...]
[(1, []),
(5, []),
(10, [2, 3, 4, 6, 7, 8, 9]),
(2, [3, 4, 6, 7, 8, 9]),
(4, [3, 6, 7, 8, 9]),
(6, [3, 7, 8, 9]),
(3, [7, 8, 9]),
(9, [7, 8]),
(12, [7, 8, 11]),
(8, [7, 11]),
(14, [7, 11, 13]),
(7, [11, 13]),
(21, [11, 13, 15, 16, 17, 18, 19, 20]),
(15, [11, 13, 16, 17, 18, 19, 20]),
(18, [11, 13, 16, 17, 19, 20]),
(16, [11, 13, 17, 19, 20]),
(20, [11, 13, 17, 19]),
(22, [11, 13, 17, 19]),
(11, [13, 17, 19]),
(33, [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])]
EKG(7):
[(<next>, [<state>]), ...]
[(1, []),
(7, []),
(14, [2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13]),
(2, [3, 4, 5, 6, 8, 9, 10, 11, 12, 13]),
(4, [3, 5, 6, 8, 9, 10, 11, 12, 13]),
(6, [3, 5, 8, 9, 10, 11, 12, 13]),
(3, [5, 8, 9, 10, 11, 12, 13]),
(9, [5, 8, 10, 11, 12, 13]),
(12, [5, 8, 10, 11, 13]),
(8, [5, 10, 11, 13]),
(10, [5, 11, 13]),
(5, [11, 13]),
(15, [11, 13]),
(18, [11, 13, 16, 17]),
(16, [11, 13, 17]),
(20, [11, 13, 17, 19]),
(22, [11, 13, 17, 19, 21]),
(11, [13, 17, 19, 21]),
(33, [13, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32]),
(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}}==
<syntaxhighlight 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.*/
if start= '' | start= "," then start=2 5 7 9 10 /* " " " " " " */
 
do s=1 for words(start); $= /*step through the specified STARTs. */
second= word(start, s); say /*obtain the second integer in the seq.*/
 
do j=1 for nums
if j<3 then do; #=1; if j==2 then #=second; end /*handle 1st & 2nd number*/
else #= ekg(#)
$= $ right(#, max(2, length(#) ) ) /*append the EKG integer to the $ list.*/
end /*j*/ /* [↑] the RIGHT BIF aligns the numbers*/
say '(start' right(second, max(2, length(second) ) )"):"$ /*display EKG seq.*/
end /*s*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
add_: do while z//j == 0; z=z%j; _=_ j; w=w+1; end; return strip(_)
/*──────────────────────────────────────────────────────────────────────────────────────*/
ekg: procedure expose $; parse arg x 1 z,,_
w=0 /*W: number of factors.*/
do k=1 to 11 by 2; j=k; if j==1 then j=2 /*divide by low primes. */
if j==9 then iterate; call add_ /*skip ÷ 9; add to list.*/
end /*k*/
/*↓ skips multiples of 3*/
do y=0 by 2; j= j + 2 + y//4 /*increment J by 2 or 4.*/
parse var j '' -1 r; if r==5 then iterate /*divisible by five ? */
if j*j>x | j>z then leave /*passed the sqrt(x) ? */
_= add_() /*add a factor to list. */
end /*y*/
j=z; if z\==1 then _= add_() /*Z¬=1? Then add──►list.*/
if _='' then _=x /*Null? Then use prime. */
do j=3; done=1
do k=1 for w
if j // word(_, k)==0 then do; done=0; leave; end
end /*k*/
if done then iterate
if wordpos(j, $)==0 then return j /*return an EKG integer.*/
end /*j*/</syntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<!-- (output is shown &nbsp; '''<sup>5</sup>/<sub>6</sub>''' &nbsp; size.) !-->
<pre style="font-size:84%">
(start 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 32 34 17 51 42 38 19 57 45 40 44 46 23 69 48 50 52 54 56 49
 
(start 5): 1 5 10 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 50 52 54 56 49 63
 
(start 7): 1 7 14 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 34 17 51 36 38 19 57 42 40 44 46 23 69 45 48 50 52 54 56 49 63
 
(start 9): 1 9 3 6 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 34 17 51 36 38 19 57 42 40 44 46 23 69 45 48 50 52 54 56 49 63
 
(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(erp,deadbuf,w){
foreach n in ([2..]w){
if(not deadrp.find(n) and e[-1]value.gcd(n)>1)
{ erp.appendset(n); dead[n]=Truew.push(buf.xplode()); buf.clear(); return(n); }
buf.append(n); // save small numbers not used yet
}
}.fp(ListRef(1,N),DictionaryList(),Walker.chain([2..N-1],True[N+1..]))).push(1,N)
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">foreach n in (T(2,5,7,9,10)){ println("EKG(%d2d): %s".fmt(n,ekgW(n).walk(10).concat(","))) }</langsyntaxhighlight>
{{out}}
<pre>
EKG( 2): L(1,2,4,6,3,9,12,8,10,5)
EKG( 5): L(1,5,10,2,4,6,3,9,12,8)
EKG( 7): L(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
</pre>
<syntaxhighlight lang="zkl">fcn convergeAt(n1,n2,etc){ ns:=vm.arglist;
<lang zkl>ekg5,ekg7, ekg5W,ekg7W := List(),List(), ekgW(5),ekgW(7);
ekg5W ekgWs:=ns.nextapply(ekgW); ekg7WekgWs.nextapply2("next"); // pop initial 1
ekgNs:=List()*vm.numArgs; // ( (ekg(n1)), (ekg(n2)) ...)
foreach e5,e7 in (ekg5W.zip(ekg7W)){
do(1_000){ // find convergence in this many terms or bail
ekg5.merge(e5); ekg7.merge(e7); // keep terms sorted
ekgN:=ekgWs.apply("next"); // (ekg(n1)[n],ekg(n2)[n] ...)
if(e5==e7 and ekg5==ekg7){ // a(n) are ==, both sequences have same terms
ekgNs.zipWith(fcn(ns,n){ ns.merge(n) },ekgN); // keep terms sorted
println("EKG(5) and EKG(7) converge at term ",ekg7.len() + 1);
// are all ekg[n]s == and both sequences have same terms?
break;
if(not ekgN.filter1('!=(ekgN[0])) and not ekgNs.filter1('!=(ekgNs[0])) ){
println("EKG(", ns.concat(","), ") converge at term ",ekgNs[0].len() + 1);
return();
}
}
println(ns.concat(",")," don't converge");
// should put limiter here
}
}</lang>
convergeAt(5,7);
convergeAt(2,5,7,9,10);</syntaxhighlight>
{{out}}
<pre>
EKG(5) and EKG(,7) converge at term 21
EKG(2,5,7,9,10) converge at term 45
</pre>
Jjuanhdez
2,169

edits

Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/284002...362115"