A094394 Odd composites m that divide Fibonacci(m)-1.

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

Offset: 1

Author

Eric Rowland, May 01 2004

Keywords

• nonn

Comments

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

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A094395, A094400.

Programs

Maple

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

Mathematica

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

PARI

main(m)=forcomposite(n=1,m,if(((n%2==1)&&(fibonacci(n)-1)%n==0),print1(n,", "))); \\ Anders Hellström, Aug 12 2015

Extensions

Offset corrected by Giovanni Resta, Jul 20 2013