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
Examples
22! = 1{1240007}27777607680000.
Links
- Paolo Xausa, Table of n, a(n) for n = 0..500
Programs
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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
Extensions
a(28)-a(29) from Pontus von Brömssen, Jan 16 2025