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Search: id:A001578
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| A001578 |
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Smallest primitive prime factor of Fibonacci number F(n).
(Formerly M0603 N0217)
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+0
8
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| 1, 1, 2, 3, 5, 1, 13, 7, 17, 11, 89, 1, 233, 29, 61, 47, 1597, 19, 37, 41, 421, 199, 28657, 23, 3001, 521, 53, 281, 514229, 31, 557, 2207, 19801, 3571, 141961, 107, 73, 9349, 135721, 2161, 2789, 211, 433494437, 43, 109441, 139, 2971215073, 1103, 97, 101
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A Fibonacci number can have more than one primitive factor; the primitive factors of F(19) are 37 and 113.
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REFERENCES
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D. Jarden, On the greatest primitive divisors of Fibonacci and Lucas numbers with prime-power subscripts, Fib. Quart. 1(#3) (1963), 15-31.
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).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000 (using Blair Kelly's data)
Blair Kelly, Fibonacci and Lucas Factorizations
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MATHEMATICA
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prms={}; Table[f=First/@FactorInteger[Fibonacci[n]]; p=Complement[f, prms]; prms=Join[prms, p]; If[p=={}, 1, First[p]], {n, 50}]
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CROSSREFS
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Cf. A086597 (number of primitive prime factors in F(n)).
Sequence in context: A132597 A030335 A030790 this_sequence A111141 A094122 A082117
Adjacent sequences: A001575 A001576 A001577 this_sequence A001579 A001580 A001581
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KEYWORD
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nonn
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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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Edited by T. D. Noe (noe(AT)sspectra.com), Apr 15 2004
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