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

1,2

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

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).

Formula

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

Example

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

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}]

Prog

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

Crossrefs

Sequence in context: A028613 A318381 A341755 * A366125 A327170 A024362

Adjacent sequences: A245512 A245513 A245514 * A245516 A245517 A245518

Keyword

nonn

Author

José de Jesús Camacho Medina, Jul 24 2014

Status

approved