A270388 a(n) = A048739(n-2) mod n.

1, 0, 0, 0, 1, 0, 0, 3, 1, 0, 8, 0, 1, 8, 0, 0, 13, 0, 8, 17, 1, 0, 0, 20, 1, 21, 8, 0, 19, 0, 0, 3, 1, 34, 8, 0, 1, 29, 8, 0, 7, 0, 8, 41, 1, 0, 0, 21, 31, 3, 8, 0, 13, 9, 8, 3, 1, 0, 20, 0, 1, 59, 0, 20, 49, 0, 8, 26, 1, 0, 0, 0, 1, 3, 8, 20, 49, 0, 48, 75, 1, 0, 56, 20, 1, 32, 24, 0, 49, 28, 8, 65, 1, 39, 0, 0, 85, 3, 68, 0

Offset: 2

Author

Altug Alkan, Mar 16 2016

Keywords

• nonn

Comments

If n is an odd prime, a(n) = 0. In other words, ((1-sqrt(2))^p + (1+sqrt(2))^p - 2) is divisible by p where p is an odd prime.

Crossrefs

Cf. A000129, A048739.

Programs

PARI

a048379(n) = my(w=quadgen(8));-1/2+(3/4+1/2*w)*(1+w)^n+(3/4-1/2*w)*(1-w)^n;
a(n) = a048379(n-2) % n;

Formula

a(n) = (((1-sqrt(2))^n + (1+sqrt(2))^n - 2) / 4) mod n, for n > 1.