A046277 Largest prime substring in n! (0 if none).

0, 0, 2, 0, 2, 2, 7, 5, 3, 3, 3, 991, 9001, 227, 8291, 1307, 209227, 68742809, 4023737, 164510040883, 24329020081, 510909421717, 1240007, 258520167388849, 4840173323, 155112100433309, 9146112660563, 694504183521607, 8344611713860501, 6199373970195454361

Offset: 0

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Examples

			22! = 1{1240007}27777607680000.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000142, A046276, A047814.

Programs

Maple

a:= n-> (s-> max(0, select(isprime, {seq(seq(parse(
    s[i..j]), i=1..j), j=1..length(s))})))(""||(n!)):
seq(a(n), n=0..30);  # Alois P. Heinz, Jan 16 2025

Mathematica

A046277[n_] := Module[{d = IntegerDigits[n!/10^IntegerExponent[n!, 10]], len, s}, len = Length[d]; While[len > 0 && (s = Select[Map[FromDigits, Partition[d, len, 1]], IntegerLength[#] == len && PrimeQ[#] &]) == {}, len--]; Max[0, s]];
Array[A046277, 30, 0] (* Paolo Xausa, Jan 16 2025 *)

Formula

a(n) = A047814(A000142(n)). - Pontus von Brömssen, Jan 16 2025

Extensions

a(28)-a(29) from Pontus von Brömssen, Jan 16 2025