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%I #25 Sep 08 2022 08:46:21
%S 4,6,7,8,10,11,14,25,34,40,44,54,62,63,66,108,190,266,299,306,310,343,
%T 350,638,726,984,1626,2223,2591,2843,3291,3694,4198,4473,4494,5128,
%U 7934,10595,12515,17433,17883,19979,23887,28847,30071,64168,79073,81971
%N Numbers k such that F(k)*F(k+1) - F(k+2) is prime, where F = A000045.
%C Primes in A059769: 7, 83, 239, 659, 4751, 12583, 228983, 9107313407, 52623175261103, 16944503546101559, 796030992711071707, 12041560801669230246323, etc.
%p with(combinat,fibonacci): select(n->isprime(fibonacci(n)*fibonacci(n+1)-fibonacci(n+2)),[$1..8000]); # _Muniru A Asiru_, Jun 12 2018
%t Select[Range[3000], PrimeQ[(Fibonacci[#] Fibonacci[# + 1] - Fibonacci[# + 2])]&]
%o (Magma) [n: n in [1..800] | IsPrime(Fibonacci(n)*Fibonacci(n+1)-Fibonacci(n+2))];
%o (PARI) isok(k) = isprime(fibonacci(k)*fibonacci(k+1) - fibonacci(k+2)); \\ _Michel Marcus_, Jun 13 2018
%Y Cf. A000045, A059769.
%K nonn
%O 1,1
%A _Vincenzo Librandi_, Jun 09 2018
%E a(38)-a(46) from _Giovanni Resta_, Jun 15 2018
%E a(47)-a(48) from _Robert Price_, Jun 18 2018
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