

A083668


Prime indices of prime Fibonacci numbers.


5



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
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OFFSET

1,1


COMMENTS

Same as A001605 without the number 4.
Contribution 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



