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

2,8

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;

Crossrefs

Cf. A000129, A048739.

Sequence in context: A143395 A090536 A187557 * A052420 A348096 A162971

Adjacent sequences: A270385 A270386 A270387 * A270389 A270390 A270391

Keyword

nonn

Author

Altug Alkan, Mar 16 2016

Status

approved