A245515 a(n) = n*floor(mod((gcd(n, Fibonacci((-1)^n + n))), 1 + n)/n) for n>=2.

1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0

Offset: 1

Author

José de Jesús Camacho Medina, Jul 24 2014

Keywords

• nonn

Comments

Sequence with many prime numbers and zeros.

The primes occurring in this sequence are given in A064739. The subsequence of composite numbers starts 1891, 2737, 2834, 4181, 6601, 6721, 8149, 13201, 13981, ... - Joerg Arndt, Nov 19 2017

Examples

			For n=1, a(1)=1; for n=2, a(2)=2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• José de Jesús Camacho Medina, Table with 140 first nonzero terms of this sequence (Una interesante fórmula generadora de 140 primos).

Programs

Magma

[n*((Gcd(n, Fibonacci((-1)^n+n)) mod (1+n)) div n): n in [1..100]]; // Vincenzo Librandi, Dec 17 2016

Maple

f:= n -> n*floor(modp((igcd(n, combinat:-fibonacci((-1)^n + n))), 1 + n)/n):
seq(f(n), n=1..100); # Robert Israel, Jul 25 2014

Mathematica

Table[n*Floor[Mod[(GCD[n, Fibonacci[(-1)^n + n]]), 1 + n]/n], {n, 1, 1890}]

PARI

a(n) = n*((gcd(n, fibonacci((-1)^n + n)) % (1 + n))\n); \\ Michel Marcus, Jul 25 2014

PARI

a(n)=gcd(n, lift(((Mod([1,1;1,0],n))^(n+(-1)^n))[1,2]))\n*n \\ Charles R Greathouse IV, Jul 25 2014

Formula

a(n) = n*floor(mod((gcd(n, fibonacci((-1)^n + n))), 1 + n)/n) for n>=1.