Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #14 Dec 07 2020 02:32:34
%S 1,1,1,1,1,2,2,1,1,2,1,2,2,1,3,2,1,4,1,1,2,1,1,8,2,2,1,3,4,6,1,1,2,3,
%T 4,3,2,1,1,2,1,2,1,2,2,9,5,1,1,2,18,1,2,1,2,3,4,1,2,10,1,2,7,1,2,2,3,
%U 2,3,2,6,1,1,2,1,1,4,2,4,2,1,20,1,2,1,1,2,2,10,1,1,1,1,1,1,1,2,20,1,6,1,18,3
%N a(1) = 1; thereafter a(n) = (p - (5|p)) divided by the smallest m such that p divides Fibonacci(m), where p is the n-th prime and (5|p) is the Legendre symbol.
%C Lucas showed that A001602 divides p-1 or p+1, according as (5|p) = 1 or -1 respectively. This is the quotient.
%H Patrick McKinley, <a href="/A116514/b116514.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (prime(n) - (5|prime(n))) / A001602(n).
%e a(6) = 2, as 13 is the 6th prime, 5 is not a quadratic residue mod 13, 13 first occurs as a prime factor of Fibonacci(7) and (13 - (-1)) / 7 = 2.
%Y Cf. A001602.
%K easy,nonn
%O 1,6
%A _Nick Krempel_, Mar 24 2006
%E a(1)=1 added by _N. J. A. Sloane_, Dec 07 2020