A155011 Sophie Germain Fibonacci prime numbers.

2, 3, 5, 89, 233, 10597999265301490732599643671505003412515860435409421932560009680142974347195483140293254396195769876129909

Offset

1,1

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

Links

Table of n, a(n) for n=1..6.

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A005478, A000045, A005384, A263880.

Sequence in context: A124121 A208226 A259378 * A065406 A111331 A205668

Adjacent sequences: A155008 A155009 A155010 * A155012 A155013 A155014

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 18 2009

Status

approved