A075737 Prime Fibonacci numbers with prime indices.

2, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241

Offset: 1

Author

Jani Melik, Oct 07 2002

Keywords

• nonn

Comments

Same as A005478 except that F(4) = 3 has been omitted.

Sequence of primes in A001519. [James R. Buddenhagen, May 20 2010]

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..20

Crossrefs

Subsequence of A030426.

Cf. A000045, A005478, A083668, A001519.

Programs

Maple

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);

Mathematica

Fibonacci[ Prime[ Select[ Range[50], PrimeQ[ Fibonacci[ Prime[ # ]]] & ]]]
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 *)

PARI

forprime(p=2,1e3,if(isprime(t=fibonacci(p)), print1(t", "))) \\ Charles R Greathouse IV, Feb 03 2014