%I #19 Sep 08 2022 08:46:09

%S 1,2,28,58,98,118,212,238,350,478,883,2660,3971,21491

%N Positive n such that Lucas(3*n) - Fibonacci(n) is a prime.

%C n=0 would give the prime 2 but positive n is required. Some terms correspond to probable primes. a(15) > 40000. - _Jens Kruse Andersen_, Aug 04 2014

%p with(combinat): A245801:=n->`if`(isprime(fibonacci(3*n+1)+fibonacci(3*n-1)-fibonacci(n)),n,NULL): seq(A245801(n), n=1..1000); # _Wesley Ivan Hurt_, Aug 04 2014

%t Select[Range[3000], PrimeQ[LucasL[3 #] - Fibonacci[#]] &]

%o (Magma) [n: n in [1..800] | IsPrime(Lucas(3*n) - Fibonacci(n))];

%o (Python)

%o import sympy

%o {print(n,end=', ') for n in range(10**3) if sympy.isprime(sympy.lucas(3*n)-sympy.fibonacci(n))} # _Derek Orr_, Aug 03 2014

%Y Cf. A000032, A000045, A014448.

%K nonn,more,hard

%O 1,2

%A _Vincenzo Librandi_, Aug 02 2014

%E 21491 from _Jens Kruse Andersen_, Aug 04 2014