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

1,1

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)

Links

Table of n, a(n) for n=1..47.

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A001605, A075737.

Sequence in context: A135832 A074781 A147545 * A176116 A063908 A154868

Adjacent sequences: A083665 A083666 A083667 * A083669 A083670 A083671

Keyword

nonn

Author

Cino Hilliard, Jun 14 2003

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

Status

approved