Step by Step solution about How to resolve the algorithm EKG sequence convergence step by step in the Go programming language

The provided Go code generates and compares two integer sequences, EKG(5) and EKG(7), to determine if they converge within a specified limit of terms.

1. Sequence Generation:

   • The code defines two arrays, starts and ekg, to generate and store the sequences.
   • Five starting values (2, 5, 7, 9, 10) are defined in starts.
   • For each starting value, an EKG sequence is generated. The algorithm to generate the sequence is as follows:
     • Initialize the sequence with the starting value.
     • Iterate over integer values, starting from 2, until limit is reached.
     • For each integer value i, check if it has not already been used in the sequence and if it shares a factor (greater than 1) with the previous element.
     • If these conditions are met, add i to the sequence. Otherwise, continue to the next integer.

2. Sequence Comparison:

   • After generating the EKG sequences, the code compares EKG(5) (index 1 in ekg) and EKG(7) (index 2 in ekg) to check for convergence.
   • The code iterates over the sequences, starting from the second term (index 2).
   • For each pair of terms at index i in both sequences, it checks if they are equal and if the sequences themselves are identical up to that point.
   • If both conditions are true, the code prints that EKG(5) and EKG(7) converge at term i+1.

3. Main Function:

   • The main function iterates over the starting values in starts to generate the EKG sequences.
   • It then iterates over the terms to compare EKG(5) and EKG(7) for convergence within the limit of 100 terms.
   • If convergence is not found within the limit, the program prints that the sequences do not converge within that limit.

In summary, this program generates integer sequences based on specific criteria and compares them to determine whether they converge within a specified number of terms. It focuses on comparing EKG(5) and EKG(7) sequences.

package main

import (
    "fmt"
    "sort"
)

func contains(a []int, b int) bool {
    for _, j := range a {
        if j == b {
            return true
        }
    }
    return false
}

func gcd(a, b int) int {
    for a != b {
        if a > b {
            a -= b
        } else {
            b -= a
        }
    }
    return a
}

func areSame(s, t []int) bool {
    le := len(s)
    if le != len(t) {
        return false
    }
    sort.Ints(s)
    sort.Ints(t)
    for i := 0; i < le; i++ {
        if s[i] != t[i] {
            return false
        }
    }
    return true
}

func main() {
    const limit = 100
    starts := [5]int{2, 5, 7, 9, 10}
    var ekg [5][limit]int

    for s, start := range starts {
        ekg[s][0] = 1
        ekg[s][1] = start
        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][:n], i) && gcd(ekg[s][n-1], i) > 1 {
                    ekg[s][n] = i
                    break
                }
            }
        }
        fmt.Printf("EKG(%2d): %v\n", start, ekg[s][:30])
    }   

    // now compare EKG5 and EKG7 for convergence
    for i := 2; 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)
            return
        }
    }
    fmt.Println("\nEKG5(5) and EKG(7) do not converge within", limit, "terms")
}