cp's OEIS Frontend

A305414 Numbers k such that F(k)*F(k+1) + F(k+2) is a prime, where F = A000045 (Fibonacci numbers).

%I A305414 #28 Sep 08 2022 08:46:21
%S A305414 1,2,3,4,5,7,8,10,11,15,16,18,29,40,55,134,159,261,276,519,1792,2045,
%T A305414 2111,2830,2878,3575,6301,7394,9432,13558,19714,21396,25731,26790,
%U A305414 28792,32070,33951,46997,63134,66272,67619,70448,75525,77994,90437
%N A305414 Numbers k such that F(k)*F(k+1) + F(k+2) is a prime, where F = A000045 (Fibonacci numbers).
%C A305414 Primes in A305412.
%C A305414 a(46) > 10^5. - _Robert Price_, Jun 18 2018
%t A305414 Select[Range[1000], PrimeQ[(Fibonacci[#] Fibonacci[# + 1] + Fibonacci[# + 2])]&]
%o A305414 (Magma) [n: n in [1..1500] | IsPrime(Fibonacci(n) * Fibonacci(n+1) + Fibonacci(n+2))];
%Y A305414 Cf. A000045, A305412.
%K A305414 nonn
%O A305414 1,2
%A A305414 _Vincenzo Librandi_, Jun 09 2018
%E A305414 More terms from _Vaclav Kotesovec_, Jun 11 2018
%E A305414 a(39) from _Giovanni Resta_, Jun 11 2018
%E A305414 a(40)-a(45) from _Robert Price_, Jun 18 2018