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A001605 Indices of prime Fibonacci numbers.
(Formerly M2309 N0911)
82
3, 4, 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, 2904353 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Some of the larger entries may only correspond to probable primes.

Since F(n) divides F(mn) (cf. A001578, A086597), all terms of this sequence are primes except for a(2) = 4 = 2 * 2 but F(2) = 1. - M. F. Hasler, Dec 12 2007

What is the next larger twin prime after F(4) = 3, F(5) = 5, F(7) = 11? It seems to be >= F(104911) (greater of a pair?) or even >= F(397379) (lesser of a pair?). - M. F. Hasler, Jan 30 2013

REFERENCES

J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260.

H. Dubner and W. Keller, New Fibonacci and Lucas Primes, Math. Comp. 68 (1999) 417-427.

Clifford A. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 54.

Paulo Ribenboim, The Little Book of Big Primes, Springer-Verlag, NY, 1991, p. 178.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..49.

David Broadhurst, Fibonacci Numbers

David Broadhurst, Proof that F(81839) is prime, NMBRTHRY maillist, 22 April 2001

Chris K. Caldwell, The Prime Glossary, Fibonacci prime

Dudley Fox, Search for Possible Fibonacci Primes

Ron Knott, Mathematics of the Fibonacci Series

Henri & Renaud Lifchitz, PRP Records.

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations

Eric Weisstein's World of Mathematics, Fibonacci Prime.

Eric Weisstein's World of Mathematics, Integer Sequence Primes.

FORMULA

Prime(i) = a(n) for some n <=> A080345(i) <= 1. - M. F. Hasler, Dec 12 2007

MATHEMATICA

Select[Range[20000], PrimeQ[Fibonacci[#]] &] (* Harvey P. Dale, Nov 20 2012 *)

PROG

(PARI) v=[3, 4]; forprime(p=5, 1e5, if(ispseudoprime(fibonacci(p)), v=concat(v, p))); v \\ Charles R Greathouse IV, Feb 14 2011

(PARI) is_A001605(n)={n==4 || isprime(n) & ispseudoprime(fibonacci(n))}  \\ - M. F. Hasler, Sep 29 2012

CROSSREFS

Cf. A005478, A000045, A001578, A086597, A080345.

Sequence in context: A081735 A227231 A107036 * A216570 A101762 A139455

Adjacent sequences:  A001602 A001603 A001604 * A001606 A001607 A001608

KEYWORD

nonn,hard,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional comments from Robert G. Wilson v, Aug 18 2000. More terms from David Broadhurst, Nov 08 2001. Two more terms (148091 and 201107) from T. D. Noe, Feb 12 2003 and Mar 04 2003.

397379 from T. D. Noe, Aug 18 2003

433781, 590041, 593689 from Henri Lifchitz submitted by Ray Chandler, Feb 11 2005

604711 from Henri Lifchitz communicated by Eric W. Weisstein, Nov 29 2005

931517, 1049897, 1285607 found by Henri Lifchitz circa Nov 01 2008 and submitted by Alexander Adamchuk, Nov 28 2008

1636007 from Henri Lifchitz 03/2009, communicated by Eric W. Weisstein, Apr 24 2009

1803059 and 1968721 from Henri Lifchitz 11/2009, submitted by Alex Ratushnyak, Aug 08 2012

a(49)=2904353 from Henri Lifchitz, Jul 15 2014

STATUS

approved

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Last modified September 20 04:05 EDT 2014. Contains 246983 sequences.