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a(n) = smallest k such that n divides Fibonacci(k-1)+3.
6

%I #17 Jun 08 2023 23:09:56

%S 1,2,1,2,4,5,13,6,17,15,7,9,19,29,17,8,23,17,15,15,13,17,12,9,18,47,

%T 41,45,11,17,27,18,17,23,77,21,10,15,25,18,25,29,34,27,17,12,21,21,13,

%U 18,33,75,59,41,17,45,33,11,14,57,35,27,45,18,75,17

%N a(n) = smallest k such that n divides Fibonacci(k-1)+3.

%H Robert Israel, <a href="/A214783/b214783.txt">Table of n, a(n) for n = 1..10000</a>

%e 1 divides F(0)+3=3. 2 divides F(1)+3=4. 3 divides F(0)+3=3. 4 divides F(1)+3=4. 5 divides F(3)+3=5.

%p A214783 := proc(n)

%p local k;

%p for k from 0 do

%p if modp(combinat[fibonacci](k)+3,n) = 0 then

%p return k;

%p end if;

%p end do:

%p end proc:

%p seq(A214783(n),n=1..80) ; # _R. J. Mathar_, Aug 08 2012

%Y Cf. A157726, A001177, A214781, A214782.

%K nonn

%O 1,2

%A _Art DuPre_, Aug 03 2012