A263880 Safe primes 2p + 1 such that p is a Fibonacci prime.

5, 7, 11, 179, 467, 21195998530602981465199287343010006825031720870818843865120019360285948694390966280586508792391539752259819

Offset: 1

Author

Jonathan Sondow, Nov 02 2015

Keywords

• nonn

Comments

Same as safe primes q whose Sophie Germain prime (2q - 1)/2 is a Fibonacci number.

No other terms up to 2*Fibonacci(2904353) + 1, according to the list of indices of 49 Fibonacci (probable) primes in A001605.

In that range, the only safe Fibonacci prime is 5. Are there larger ones?

There are six primes 2p + 1 such that p is a Fibonacci prime, namely, a(1) through a(6). By contrast, in the same range there are only two primes 2p - 1 such that p is a Fibonacci prime, namely, 2p - 1 = 3 and 5, for p = 2 and 3. Is there some modular restriction to explain this bias in favor of 2p + 1 over 2p - 1 among Fibonacci primes p?

Examples

			179 is in the sequence because it is prime and (179 - 1)/2 = 89 = Fibonacci(11), which is also prime.
		

Links

• Wikipedia, Fibonacci prime
• Wikipedia, Safe prime
• Wikipedia, Sophie Germain prime

Crossrefs

Cf. A000045, A005384, A005385, A005478, A155011.

Programs

Mathematica

2 * Select[Fibonacci[Range[2000]], And @@ PrimeQ[{#, 2 # + 1}] &] + 1

Formula

a(n) = 2*A155011(n) + 1.