A345666 Composite numbers whose largest prime substring is greater than the record of all previous terms.

12, 15, 27, 110, 117, 119, 123, 129, 141, 143, 147, 153, 159, 161, 171, 183, 189, 297, 1010, 1030, 1070, 1090, 1113, 1127, 1131, 1137, 1139, 1149, 1157, 1167, 1173, 1179, 1191, 1197, 1199, 1211, 1227, 1233, 1239, 1241, 1251, 1257, 1263, 1269, 1271, 1281, 1293

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Example

a(1)=12 is the first composite containing a prime substring. Its largest prime substring is A345667(1)=2. It is the first nonzero composite index of A047814.

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, n]], {n, 10000}]; lst (* Giorgos Kalogeropoulos, Jun 25 2021 *)

Prog

(Python)
def trojan_composites(limit_maxval=None, limit_terms=None, verbose=True):
    from sympy import isprime
    num = 1
    best = 0
    found = []
    while (not limit_maxval or num <= 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(best)), -1):
                candidate = max(filter(isprime, {int(string[i:i + length - 1]) for i in range(len(string) - length + 2)}), default=0)
                if candidate:
                    if candidate > best:
                        best = candidate
                        found.append(num)
                        if verbose:
                            print(num, end=', ', flush=True)
                break
    if verbose:
        print()
    return found
trojan_composites(limit_terms=7) #[12, 15, 27, 110, 117, 119, 123]

Crossrefs

Cf. A002808, A047814, A345667 (corresponding prime substrings).

Sequence in context: A357867 A350807 A124521 * A369005 A134221 A179148

Adjacent sequences: A345663 A345664 A345665 * A345667 A345668 A345669

Keyword

nonn,base

Author

Eyal Gruss, Jun 21 2021

Status

approved