A359808 - OEIS

%I #16 Feb 16 2025 08:34:04

%S 1,1,5,19,101,619,4421,35899,79,3301819,13,29,47,23,1226280710981,53,

%T 47,2683,115578717622022981,8969,113,79,85439,12203,59,1657,127,61,

%U 661,47,173183,1117,83,4729,37,103,2858548279,59,67,431,32656499591185747972776747396512425885838364422981

%N 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 a(n) is the least prime factor of A005165(n) (unless A005165(n) = 1, in which case a(n) = 1).

%C a(n) = A005165(n) iff n is a term in A001272 or n < 2.

%H Jon E. Schoenfield, <a href="/A359808/b359808.txt">Table of n, a(n) for n = 1..149</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlternatingFactorial.html">Alternating Factorial</a>

%F a(n) = A020639(A005165).

%p b:= proc(n) option remember; `if`(n=0, 0, n!-b(n-1)) end:

%p a:= n-> `if`(n<3, 1, min(numtheory[factorset](b(n)))):

%p seq(a(n), n=1..41);  # _Alois P. Heinz_, Jan 13 2023

%t a[n_] :=  FactorInteger[AlternatingFactorial[n]][[1, 1]];

%t Table[a[n], {n, 1, 41}] (* _Jean-François Alcover_, Jan 24 2023 *)

%Y Cf. A001272, A005165, A020639.

%K nonn

%O 1,3

%A _Jon E. Schoenfield_, Jan 13 2023