A094394 - OEIS

%I #33 Aug 29 2021 11:59:48

%S 323,2737,4181,6479,6721,7743,11663,13201,15251,18407,19043,23407,

%T 27071,34561,34943,35207,39203,44099,47519,51841,51983,53663,54839,

%U 64079,64681,65471,67861,68251,72831,78089,79547,82983,86063,90061,94667

%N Odd composites m that divide Fibonacci(m)-1.

%C No terms satisfy the Fermat criterion 2^(a(n)-1) mod a(n) = 1. - _Gary Detlefs_, May 25 2014

%C 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

%H Giovanni Resta, <a href="/A094394/b094394.txt">Table of n, a(n) for n = 1..1000</a>

%p with(combinat):test:=n->(fibonacci(n)-1) mod n= 0:

%p select(test and not isprime ,[seq(2*k+1,k=1..10000)]); # _Robert FERREOL_, Jul 14 2015

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

%o (PARI) main(m)=forcomposite(n=1,m,if(((n%2==1)&&(fibonacci(n)-1)%n==0),print1(n,", "))); \\ _Anders Hellström_, Aug 12 2015

%Y Cf. A094395, A094400.

%K nonn

%O 1,1

%A _Eric Rowland_, May 01 2004

%E Offset corrected by _Giovanni Resta_, Jul 20 2013