A337307 a(1) = 1; a(n) = 1 + Product_{k=1..n-1} a(k) (mod n-1).

1, 1, 2, 3, 3, 4, 1, 3, 1, 1, 7, 6, 1, 12, 1, 10, 1, 12, 1, 3, 1, 1, 21, 12, 1, 6, 21, 1, 1, 15, 1, 20, 1, 31, 15, 1, 1, 32, 13, 1, 1, 18, 1, 7, 25, 1, 17, 38, 1, 1, 1, 1, 1, 26, 1, 6, 1, 1, 29, 47, 1, 42, 1, 1, 1, 1, 61, 26, 1, 25, 1, 21, 1, 64, 21, 1, 1, 29, 1, 18

Offset: 1

Author

Matt Donahoe, Aug 22 2020

Keywords

• nonn

Comments

Note that the running product for each a(n) is incrementally computed mod n-1.

Crossrefs

Inspired by A066910.

Cf. A129871 (without the mod operation).

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = 1 + Mod[Product[a[k], {k, 1, n - 1}], n - 1]; Array[a, 100] (* Amiram Eldar, Aug 22 2020 *)

PARI

lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = 1 + prod(k=1, n-1, va[k]) % (n-1);); va;} \\ Michel Marcus, Aug 23 2020

Python

def f(n):
    if n == 1: return 1
    a = 1
    for k in range(1, n):
        a = a * f(k) % (n - 1)
    return a + 1