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Largest prime substring in n! (0 if none).
4

%I #23 Jan 16 2025 19:36:53

%S 0,0,2,0,2,2,7,5,3,3,3,991,9001,227,8291,1307,209227,68742809,4023737,

%T 164510040883,24329020081,510909421717,1240007,258520167388849,

%U 4840173323,155112100433309,9146112660563,694504183521607,8344611713860501,6199373970195454361

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

%H Paolo Xausa, <a href="/A046277/b046277.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = A047814(A000142(n)). - _Pontus von Brömssen_, Jan 16 2025

%e 22! = 1{1240007}27777607680000.

%p a:= n-> (s-> max(0, select(isprime, {seq(seq(parse(

%p s[i..j]), i=1..j), j=1..length(s))})))(""||(n!)):

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Jan 16 2025

%t 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]];

%t Array[A046277, 30, 0] (* _Paolo Xausa_, Jan 16 2025 *)

%Y Cf. A000142, A046276, A047814.

%K nonn,base

%O 0,3

%A _Patrick De Geest_, Jun 15 1998

%E a(28)-a(29) from _Pontus von Brömssen_, Jan 16 2025