A155011 Sophie Germain Fibonacci prime numbers.

2, 3, 5, 89, 233, 10597999265301490732599643671505003412515860435409421932560009680142974347195483140293254396195769876129909

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

Keywords

• nonn

Comments

2*2+1=5, 2*3+1=7, 2*5+1=11, ...

No additional terms up through Fibonacci(10000). - Harvey P. Dale, Nov 26 2013

No additional terms up through Fibonacci(50000). - Chai Wah Wu, Nov 04 2015

Crossrefs

Cf. A005478, A000045, A005384, A263880.

Programs

Mathematica

a={};Do[f=Fibonacci[n];If[PrimeQ[f],If[PrimeQ[2*f+1],AppendTo[a,f]]],{n,3*6!}];a
  Select[Fibonacci[Range[2000]],And@@PrimeQ[{#,2#+1}]&] (* Harvey P. Dale, Nov 26 2013 *)

Python

from gmpy2 import is_prime
A155011_list = []
a, b, a2, b2 = 0, 1, 1, 3
for _ in range(10**6):
    if is_prime(b) and is_prime(b2):
        A155011_list.append(b)
    a, b, a2, b2 = b, a+b, b2, a2+b2-1 # Chai Wah Wu, Nov 04 2015

Formula

a(n) = (A263880(n) - 1)/2. - Jonathan Sondow, Nov 04 2015