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EKG sequence convergence: Difference between revisions

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EKG sequence convergence (view source)

Revision as of 08:23, 17 March 2024

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# [[Greatest common divisor]]
# [[Sieve of Eratosthenes]]
# [[Yellowstone sequence]]
<br>
;Reference:
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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>
 
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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}}==
Line 1,020 ⟶ 1,158:
 
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}}==
Line 1,356 ⟶ 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>
 
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{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./sort" for Sort
import "./math" for Int
import "./fmt" for Fmt
 
var areSame = Fn.new { |s, t|
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