A270388 - OEIS

%I #12 Mar 16 2016 17:02:16

%S 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,

%T 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,

%U 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

%N a(n) = A048739(n-2) mod n.

%C 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.

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

%o (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;

%o a(n) = a048379(n-2) % n;

%Y Cf. A000129, A048739.

%K nonn

%O 2,8

%A _Altug Alkan_, Mar 16 2016