A345667 a(n) is the largest prime substring of A345666(n).
2, 5, 7, 11, 17, 19, 23, 29, 41, 43, 47, 53, 59, 61, 71, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 173, 179, 191, 197, 199, 211, 227, 233, 239, 241, 251, 257, 263, 269, 271, 281, 293, 311, 313, 317, 331, 337, 347, 349, 353, 359
Offset: 1
Examples
a(4) = 11 is the largest prime substring of A345666(4) = 110.
Programs
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Mathematica
lst={};max=m=0;Do[If[!PrimeQ@n,If[IntegerQ[s=Max@Select[FromDigits/@Subsequences@IntegerDigits@n,PrimeQ]],m=s]];If[m>max,max=m;AppendTo[lst,s]],{n,10000}];lst (* Giorgos Kalogeropoulos, Jun 25 2021 *) -
Python
def trojan_composites_records(limit_maxval=None, limit_terms=None, verbose=True): from sympy import isprime num = 1 found = [] while (not limit_maxval or not found or found[-1] <= limit_maxval) and (not limit_terms or len(found) < limit_terms): num += 1 if not isprime(num): string = str(num) for length in range(len(string), len(str(found[-1])) if found else 1, -1): candidate = max(filter(isprime, {int(string[i:i + length - 1]) for i in range(len(string) - length + 2)}), default=0) if candidate: if not found or candidate > found[-1]: if limit_maxval and candidate > limit_maxval: if verbose: print() return found found.append(candidate) if verbose: print(candidate, end=', ', flush=True) break if verbose: print() return found trojan_composites_records(limit_terms=7) # [2, 5, 7, 11, 17, 19, 23]