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A094401 Composite n such that n divides both Fibonacci(n-1) and Fibonacci(n) - 1. 7
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; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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. [T. D. Noe, Jan 09 2009]

LINKS

T. D. Noe and Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 200 terms from T. D. Noe)

Eric Weisstein, MathWorld: Fibonacci Q-Matrix,

MATHEMATICA

Select[Range[2, 50000], ! PrimeQ[ # ] && Mod[Fibonacci[ # - 1], # ] == 0 && Mod[Lucas[ # ] - 1, # ] == 0 &]

CROSSREFS

Cf. A005845, A069106, A094394, A094400.

Sequence in context: A253987 A258904 A221976 * A035774 A107570 A237680

Adjacent sequences:  A094398 A094399 A094400 * A094402 A094403 A094404

KEYWORD

nonn

AUTHOR

Eric Rowland, May 01 2004

EXTENSIONS

More terms from Ryan Propper, Sep 24 2005

STATUS

approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)