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Search: id:A001605
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| A001605 |
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Indices of prime Fibonacci numbers.
(Formerly M2309 N0911)
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+0
58
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 (Maximilian.Hasler(AT)gmail.com), Dec 12 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260.
D. Broadhurst, Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), 22 April 2001
H. Dubner and W. Keller, New Fibonacci and Lucas Primes, Math. Comp. 68 (1999) 417-427
Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
C. Pickover, Mazes for the Mind, St. Martin's Press, NY, 1992, p. 350.
P. Ribenboim, The Little Book of Big Primes, Springer-Verlag, NY, 1991, p. 178.
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 54.
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LINKS
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David Broadhurst, Fibonacci Numbers
David Broadhurst, Proof that F(81839) is prime
C. K. Caldwell, The Prime Glossary, Fibonacci prime
Dudley Fox, Search for Possible Fibonacci Primes
R. Knott, Mathematics of the Fibonacci Series
Henri & Renaud Lifchitz, PRP Records.
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.
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FORMULA
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Prime(i) = a(n) for some n <=> A080345(i) <= 1. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Dec 12 2007
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MATHEMATICA
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lst={}; Do[f=Fibonacci[n]; If[PrimeQ[f], AppendTo[lst, n]], {n, 1, 10^4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 14 2008]
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CROSSREFS
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Cf. A005478.
Cf. A000045, A001578, A086597, A080345.
Sequence in context: A140826 A081735 A107036 this_sequence A101762 A139455 A095880
Adjacent sequences: A001602 A001603 A001604 this_sequence A001606 A001607 A001608
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KEYWORD
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nonn,hard,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 18 2000. More terms from David Broadhurst, Nov 08 2001. Two more terms (148091 and 201107) from T. D. Noe (noe(AT)sspectra.com), Feb 12 2003 and Mar 04 2003.
397379 from T. D. Noe (noe(AT)sspectra.com), Aug 18 2003
433781, 590041, 593689 from Henri Lifchitz (HLifchitz(AT)compuserve.com) submitted by Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 11 2005
604711 from Henri Lifchitz (HLifchitz(AT)compuserve.com) communicated by Eric Weisstein (eric(AT)weisstein.com), Nov 29 2005
931517, 1049897, 1285607 found by Henri Lifchitz circa Nov 01 2008 and submitted by Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 28 2008
1636007 from Henri Lifchitz 03/2009, communicated by Eric W. Weisstein (eric(AT)weisstein.com), Apr 24 2009
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