A270388 - OEIS

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

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OFFSET

2,8

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.

LINKS

Table of n, a(n) for n=2..101.

FORMULA

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

PROG

(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;