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A083668
Prime indices of prime Fibonacci numbers.
8
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)
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
Sequence in context: A135832 A074781 A147545 * A176116 A063908 A154868
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