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A359808 a(n) is the least prime factor of the alternating factorial n! - (n-1)! + (n-2)! - ... 1! for n > 2; a(1) = a(2) = 1.

%I A359808 #16 Feb 16 2025 08:34:04
%S A359808 1,1,5,19,101,619,4421,35899,79,3301819,13,29,47,23,1226280710981,53,
%T A359808 47,2683,115578717622022981,8969,113,79,85439,12203,59,1657,127,61,
%U A359808 661,47,173183,1117,83,4729,37,103,2858548279,59,67,431,32656499591185747972776747396512425885838364422981
%N A359808 a(n) is the least prime factor of the alternating factorial n! - (n-1)! + (n-2)! - ... 1! for n > 2; a(1) = a(2) = 1.
%C A359808 a(n) is the least prime factor of A005165(n) (unless A005165(n) = 1, in which case a(n) = 1).
%C A359808 a(n) = A005165(n) iff n is a term in A001272 or n < 2.
%H A359808 Jon E. Schoenfield, <a href="/A359808/b359808.txt">Table of n, a(n) for n = 1..149</a>
%H A359808 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlternatingFactorial.html">Alternating Factorial</a>
%F A359808 a(n) = A020639(A005165).
%p A359808 b:= proc(n) option remember; `if`(n=0, 0, n!-b(n-1)) end:
%p A359808 a:= n-> `if`(n<3, 1, min(numtheory[factorset](b(n)))):
%p A359808 seq(a(n), n=1..41);  # _Alois P. Heinz_, Jan 13 2023
%t A359808 a[n_] :=  FactorInteger[AlternatingFactorial[n]][[1, 1]];
%t A359808 Table[a[n], {n, 1, 41}] (* _Jean-François Alcover_, Jan 24 2023 *)
%Y A359808 Cf. A001272, A005165, A020639.
%K A359808 nonn
%O A359808 1,3
%A A359808 _Jon E. Schoenfield_, Jan 13 2023