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A075737 Prime Fibonacci numbers with prime indices.

%I A075737 #20 Oct 13 2019 06:12:48
%S A075737 2,5,13,89,233,1597,28657,514229,433494437,2971215073,
%T A075737 99194853094755497,1066340417491710595814572169,
%U A075737 19134702400093278081449423917,475420437734698220747368027166749382927701417016557193662268716376935476241
%N A075737 Prime Fibonacci numbers with prime indices.
%C A075737 Same as A005478 except that F(4) = 3 has been omitted.
%C A075737 Sequence of primes in A001519. [_James R. Buddenhagen_, May 20 2010]
%H A075737 T. D. Noe, <a href="/A075737/b075737.txt">Table of n, a(n) for n = 1..20</a>
%e A075737 5 is a prime and fibonacci(5)=5 is also a prime, 7 is a prime and fibonacci(7)=13 is also a prime, but 2 is a prime and fibonacci(2)=1 is not a prime.
%p A075737 with(combinat, fibonacci): fib_supM_pra := proc(n); if (isprime(n)='true') then if (isprime(fibonacci(n))='true') then RETURN(fibonacci(n)); fi; fi; end: seq(fib_supM_pra(i), i=1..500);
%t A075737 Fibonacci[ Prime[ Select[ Range[50], PrimeQ[ Fibonacci[ Prime[ # ]]] & ]]]
%t A075737 Module[{nn=500,fibs},fibs=Fibonacci[Range[nn]];Select[Pick[fibs,Table[ If[ PrimeQ[n],1,0],{n,nn}],1],PrimeQ]] (* _Harvey P. Dale_, Sep 13 2018 *)
%o A075737 (PARI) forprime(p=2,1e3,if(isprime(t=fibonacci(p)), print1(t", "))) \\ _Charles R Greathouse IV_, Feb 03 2014
%Y A075737 Subsequence of A030426.
%Y A075737 Cf. A000045, A005478, A083668, A001519.
%K A075737 nonn
%O A075737 1,1
%A A075737 _Jani Melik_, Oct 07 2002