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A094394
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Odd composites m that divide Fibonacci(m)-1.
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10
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323, 2737, 4181, 6479, 6721, 7743, 11663, 13201, 15251, 18407, 19043, 23407, 27071, 34561, 34943, 35207, 39203, 44099, 47519, 51841, 51983, 53663, 54839, 64079, 64681, 65471, 67861, 68251, 72831, 78089, 79547, 82983, 86063, 90061, 94667
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OFFSET
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1,1
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COMMENTS
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No terms satisfy the Fermat criterion 2^(a(n)-1) mod a(n) = 1. - Gary Detlefs, May 25 2014
For each prime p, Fibonacci(p) = 5^((p-1)/2) mod p, so p divides Fibonacci(p) - 1 for each prime p=10k+-1. Hence it is interesting to seek also nonprimes with the same property, a motivation for this sequence. - Robert FERREOL, Jul 14 2015
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LINKS
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MAPLE
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with(combinat):test:=n->(fibonacci(n)-1) mod n= 0:
select(test and not isprime , [seq(2*k+1, k=1..10000)]); # Robert FERREOL, Jul 14 2015
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MATHEMATICA
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Select[Range[2, 50000], OddQ[#] && ! PrimeQ[#] && Mod[Fibonacci[#] - 1, #] == 0 &]
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PROG
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(PARI) main(m)=forcomposite(n=1, m, if(((n%2==1)&&(fibonacci(n)-1)%n==0), print1(n, ", "))); \\ Anders Hellström, Aug 12 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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