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
KEYWORD
nonn
AUTHOR
José de Jesús Camacho Medina, Jul 24 2014
STATUS
approved