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%I #43 Oct 01 2021 11:54:23
%S 5,7,13,433,571
%N Numbers n such that F(n) and F(n-2) are both prime where F(n) = A000045(n).
%C a(6) > 2904353. - _Daniel Suteu_, Dec 23 2016
%C Terms n of A001605 such that n-2 is also a term of A001605. Surprisingly, the first 4 terms minus 2, { 3, 5, 11, 431 }, are the first four terms of A101315 which also relates to simultaneously prime { m+2, F(m) and F(m)+2 }, but where F is a different function, m -> (m-1)^2 + 1. - _M. F. Hasler_, Dec 24 2016
%C Larger primes of the Fibonacci prime pairs in A073340. - _Bobby Jacobs_, Jan 18 2017
%F a(n) = A281087(n) + 2. - _Bobby Jacobs_, Jan 18 2017
%e 13 is a term because Fibonacci(13) = 233 and Fibonacci(11) = 89 are both prime.
%t Select[Range[10^4], Times @@ Boole@ Map[PrimeQ@ Fibonacci@ # &, {#, # - 2}] > 0 &] (* _Michael De Vlieger_, Jan 21 2017 *)
%t Flatten[Position[Partition[Fibonacci[Range[580]],3,1],_?(AllTrue[ {#[[1]],#[[3]]},PrimeQ]&),1,Heads->False]]+2 (* _Harvey P. Dale_, Oct 01 2021 *)
%o (PARI) isok(n) = isprime(fibonacci(n)) && isprime(fibonacci(n-2)); \\ _Michel Marcus_, Jan 14 2017
%Y Cf. A000045, A001605, A006512, A073340, A101315, A281087.
%K more,nonn
%O 1,1
%A _Altug Alkan_, Dec 18 2016
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