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

1,1

Links

Table of n, a(n) for n=1..56.

Example

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

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 *)

Prog

(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]

Crossrefs

Cf. A002808, A345666. Subset of A047814.

Sequence in context: A309290 A023238 A194991 * A319596 A235480 A049042

Adjacent sequences: A345664 A345665 A345666 * A345668 A345669 A345670

Keyword

nonn,base

Author

Eyal Gruss, Jun 21 2021

Status

approved