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A214783 a(n) = smallest k such that n divides Fibonacci(k-1)+3.

%I A214783 #17 Jun 08 2023 23:09:56
%S A214783 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 A214783 41,45,11,17,27,18,17,23,77,21,10,15,25,18,25,29,34,27,17,12,21,21,13,
%U A214783 18,33,75,59,41,17,45,33,11,14,57,35,27,45,18,75,17
%N A214783 a(n) = smallest k such that n divides Fibonacci(k-1)+3.
%H A214783 Robert Israel, <a href="/A214783/b214783.txt">Table of n, a(n) for n = 1..10000</a>
%e A214783 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 A214783 := proc(n)
%p A214783         local k;
%p A214783         for k from 0 do
%p A214783                 if modp(combinat[fibonacci](k)+3,n) = 0 then
%p A214783                         return k;
%p A214783                 end if;
%p A214783         end do:
%p A214783 end proc:
%p A214783 seq(A214783(n),n=1..80) ; # _R. J. Mathar_, Aug 08 2012
%Y A214783 Cf. A157726, A001177, A214781, A214782.
%K A214783 nonn
%O A214783 1,2
%A A214783 _Art DuPre_, Aug 03 2012