cp's OEIS Frontend

A023164 Numbers k such that Fibonacci(k) == -3 (mod k).

%I A023164 #20 Apr 11 2022 12:21:19
%S A023164 1,2,8,68,92,188,212,332,428,452,548,668,692,788,908,932,1028,1052,
%T A023164 1172,1268,1292,1388,1412,1508,1532,1772,1868,2012,2074,2156,2228,
%U A023164 2252,2314,2348,2372,2468,2588,2612,2708,2732,2972,3092,3188,3308,3428,3452,3548
%N A023164 Numbers k such that Fibonacci(k) == -3 (mod k).
%C A023164 Includes 4*p for primes p with p == 17 or 23 (mod 30). - _Robert Israel_, May 11 2021
%H A023164 Robert Israel, <a href="/A023164/b023164.txt">Table of n, a(n) for n = 1..2000</a>
%p A023164 fpp:= n -> mpow(n-1, n)[2, 2]:
%p A023164 M:= <<0, 1>|<1, 1>>:
%p A023164 mpow:= proc(n, p)
%p A023164   if n = 0 then <<1, 0>|<0, 1>>
%p A023164   elif n::even then procname(n/2, p)^2 mod p
%p A023164   else  procname((n-1)/2, p)^2 . M mod p
%p A023164   fi
%p A023164 end proc:
%p A023164 select(t -> fpp(t)+3 mod t = 0, [$1..10000]); # _Robert Israel_, May 11 2021
%t A023164 Select[Range[3600],Mod[Fibonacci[#]+3,#]==0&] (* _Harvey P. Dale_, Sep 21 2021 *)
%Y A023164 Cf. A000045, A002708.
%K A023164 nonn
%O A023164 1,2
%A A023164 _David W. Wilson_
%E A023164 Definition clarified by _N. J. A. Sloane_, Sep 21 2021