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.

1, 1, 5, 19, 101, 619, 4421, 35899, 79, 3301819, 13, 29, 47, 23, 1226280710981, 53, 47, 2683, 115578717622022981, 8969, 113, 79, 85439, 12203, 59, 1657, 127, 61, 661, 47, 173183, 1117, 83, 4729, 37, 103, 2858548279, 59, 67, 431, 32656499591185747972776747396512425885838364422981

Offset: 1

Author

Jon E. Schoenfield, Jan 13 2023

Keywords

• nonn

Comments

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

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

Links

• Jon E. Schoenfield, Table of n, a(n) for n = 1..149
• Eric Weisstein's World of Mathematics, Alternating Factorial

Crossrefs

Cf. A001272, A005165, A020639.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 0, n!-b(n-1)) end:
a:= n-> `if`(n<3, 1, min(numtheory[factorset](b(n)))):
seq(a(n), n=1..41);  # Alois P. Heinz, Jan 13 2023

Mathematica

a[n_] :=  FactorInteger[AlternatingFactorial[n]][[1, 1]];
Table[a[n], {n, 1, 41}] (* Jean-François Alcover, Jan 24 2023 *)

Formula

a(n) = A020639(A005165).