%I #16 Aug 20 2021 04:21:06
%S 323,377,2834,3827,6479,11663,18407,19043,20999,23407,25877,27323,
%T 34943,35207,39203,44099,47519,50183,51983,53663,60377,65471,78089,
%U 79547,81719,82983,84279,84419,86063,90287,94667,104663,109871,121103,121393
%N Numbers k that divide Fibonacci(k+1) but do not divide Fibonacci(k) + 1.
%H Giovanni Resta, <a href="/A094412/b094412.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Range[50000], ! Mod[Fibonacci[ # ] + 1, # ] == 0 && Mod[Fibonacci[ # + 1], # ] == 0 &]
%t Select[Range[122000],Divisible[{Fibonacci[#+1],Fibonacci[#]+1},#]=={True,False}&] (* _Harvey P. Dale_, Apr 16 2019 *)
%o (PARI) fibmod(n,m)=(Mod([0,1;1,1],m)^n*[0;1])[1,1]
%o is(n)=fibmod(n+1,n)==0 && fibmod(n,n)!=-1 \\ _Charles R Greathouse IV_, Nov 04 2016
%Y Cf. A000045, A069107, A094395, A094401, A094411.
%K nonn
%O 1,1
%A _Eric Rowland_, May 01 2004