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Search: id:A094401
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| A094401 |
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Composite n such that n divides both Fibonacci(n-1) and Fibonacci(n) - 1. |
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+0
6
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| 2737, 4181, 6721, 13201, 15251, 34561, 51841, 64079, 64681, 67861, 68251, 90061, 96049, 97921, 118441, 146611, 163081, 179697, 186961, 194833, 197209, 219781, 252601, 254321, 257761, 268801, 272611, 283361, 302101, 303101, 327313, 330929
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Composite n such that Q^(n-1) = I (mod n), where Q is the Fibonacci matrix {{1,1},{1,0}} and I is the identity matrix. The identity is also true for the primes congruent to 1 or 4 (mod 5), which is sequence A045468. The period of Q^k (mod n) is the same as the period of the Fibonacci numbers F(k) (mod n), A001175. Hence the terms in this sequence are the composite n such that A001175(n) divides n-1. [From T. D. Noe (noe(AT)sspectra.com), Jan 09 2009]
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Eric Weisstein, MathWorld: Fibonacci Q-Matrix, [From T. D. Noe (noe(AT)sspectra.com), Jan 09 2009]
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MATHEMATICA
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Select[Range[2, 50000], ! PrimeQ[ # ] && Mod[Fibonacci[ # - 1], # ] == 0 && Mod[Lucas[ # ] - 1, # ] == 0 &]
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CROSSREFS
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Cf. A005845, A069106, A094394, A094400.
Sequence in context: A145647 A045155 A122473 this_sequence A035774 A107570 A094497
Adjacent sequences: A094398 A094399 A094400 this_sequence A094402 A094403 A094404
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KEYWORD
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nonn
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AUTHOR
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Eric S Rowland (erowland(AT)math.rutgers.edu), May 01 2004
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EXTENSIONS
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More terms from Ryan Propper (rpropper(AT)stanford.edu), Sep 24 2005
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