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

0,3

Links

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

Formula

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

Example

22! = 1{1240007}27777607680000.

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 *)

Crossrefs

Cf. A000142, A046276, A047814.

Sequence in context: A284570 A256847 A372023 * A053571 A307391 A129883

Adjacent sequences: A046274 A046275 A046276 * A046278 A046279 A046280

Keyword

nonn,base

Author

Patrick De Geest, Jun 15 1998

Extensions

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

Status

approved