A083668 Prime indices of prime Fibonacci numbers.

3, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571, 2971, 4723, 5387, 9311, 9677, 14431, 25561, 30757, 35999, 37511, 50833, 81839, 104911, 130021, 148091, 201107, 397379, 433781, 590041, 593689, 604711, 931517, 1049897, 1285607, 1636007, 1803059, 1968721

Offset: 1

Author

Cino Hilliard, Jun 14 2003

Keywords

• nonn

Comments

Same as A001605 without the number 4.

From V. Raman, Oct 04 2012: (Start)

Also the indices of prime Fibonacci numbers which can be written as the sum of two positive squares.

The Fibonacci numbers F(6k+1) and F(6k+5) are congruent to 1 (mod 4).

(End)

Examples

			For Fib(n) to be prime, n must be prime, except for n=4. The first 9 primes are: 2, 3, 5, 7, 11, 13, 17, 19 and 23. The corresponding Fibonacci numbers are: 1, 2, 5, 13, 89, 233, 1597, 4181 and 28657. All of these are prime except Fib(2) = 1 and Fib(19) = 4181. So the first 7 terms of this sequence are 3, 5, 7, 11, 13, 17 and 23.
		

Crossrefs

Cf. A001605, A075737.

Programs

Mathematica

Do[ If[ PrimeQ[ Fibonacci[ Prime[n]]], Print[ Prime[n]]], {n, 1, 1000}]

PARI

pif(n) = { forprime(x=2,n, if(isprime(fibonacci(x)), print1(x" "))) }

PARI

is(p)=isprime(p) & ispseudoprime(fibonacci(p))  \\ Charles R Greathouse IV, Sep 19 2012

Extensions

More terms from Zak Seidov, Aug 31 2006

Replaced the erroneous example Harry J. Smith, Jan 16 2009

Terms a(42) to a(47) added by V. Raman, Oct 04 2012

Definition and wrong statement in example corrected by M. F. Hasler, Oct 08 2012