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

%I A245515 #51 Sep 08 2022 08:46:08
%S A245515 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,
%T A245515 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,
%U A245515 0,0,0,0,0,71,0,0,0,0,0,0,0,79,0,0,0,0,0,0
%N A245515 a(n) = n*floor(mod((gcd(n, Fibonacci((-1)^n + n))), 1 + n)/n) for n>=2.
%C A245515 Sequence with many prime numbers and zeros.
%C A245515 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
%H A245515 Charles R Greathouse IV, <a href="/A245515/b245515.txt">Table of n, a(n) for n = 1..10000</a>
%H A245515 José de Jesús Camacho Medina, <a href="http://matematicofresnillense.blogspot.fr/2013/07/una-interesante-formula-generadora-de.html">Table with 140 first nonzero terms of this sequence</a> (Una interesante fórmula generadora de 140 primos).
%F A245515 a(n) = n*floor(mod((gcd(n, fibonacci((-1)^n + n))), 1 + n)/n) for n>=1.
%e A245515 For n=1, a(1)=1; for n=2, a(2)=2.
%p A245515 f:= n -> n*floor(modp((igcd(n, combinat:-fibonacci((-1)^n + n))), 1 + n)/n):
%p A245515 seq(f(n), n=1..100); # _Robert Israel_, Jul 25 2014
%t A245515 Table[n*Floor[Mod[(GCD[n, Fibonacci[(-1)^n + n]]), 1 + n]/n], {n, 1, 1890}]
%o A245515 (PARI) a(n) = n*((gcd(n, fibonacci((-1)^n + n)) % (1 + n))\n); \\ _Michel Marcus_, Jul 25 2014
%o A245515 (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
%o A245515 (Magma) [n*((Gcd(n, Fibonacci((-1)^n+n)) mod (1+n)) div n): n in [1..100]]; // _Vincenzo Librandi_, Dec 17 2016
%K A245515 nonn
%O A245515 1,2
%A A245515 _José de Jesús Camacho Medina_, Jul 24 2014