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

Author

Eyal Gruss, Jun 21 2021

Keywords

• nonn
• base

Examples

			a(4) = 11 is the largest prime substring of A345666(4) = 110.
		

Crossrefs

Cf. A002808, A345666. Subset of A047814.

Programs

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]