Step by Step solution about How to resolve the algorithm EKG sequence convergence step by step in the Mathematica/Wolfram Language programming language

The provided Wolfram code defines functions and calculates the next number in a sequence based on the last number and specific properties. Here's a breakdown of the code:

1. NextInSequence Function:

• It takes a list seq as input, representing a sequence of numbers.
• It calculates the last number of the sequence (last), the maximum number in the sequence (max), and a list of missing numbers (holes) in the sequence.
• It selects the first number in holes that is not coprime with last. Coprime numbers are numbers that have no common factors other than 1. If no such number is found, it proceeds to the next step.
• If no suitable number is found in holes, it starts from max and increments it until it finds a coprime number.
• The function returns the new sequence with the next number appended to it.

2. EKGSequence Function:

• It takes two integer arguments: start (the starting number) and n (the number of terms to generate).
• It uses the Nest function to apply the NextInSequence function n - 2 times to the initial sequence {1, start}, generating the desired sequence.

3. Generating and Displaying Tables:

• The code creates a table showing EKGSequence for different starting numbers (s). The table is displayed as a grid.

4. Length of Convergence:

• It calculates the length of convergence between two EKGSequence sequences (starting at 5 and 7). It first finds the common sequence length (len) and then trims the sequences accordingly.
• The code returns the length of the trimmed sequence plus 1, which represents the length of convergence between the two sequences.

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