A023164 - OEIS

%I #20 Apr 11 2022 12:21:19

%S 1,2,8,68,92,188,212,332,428,452,548,668,692,788,908,932,1028,1052,

%T 1172,1268,1292,1388,1412,1508,1532,1772,1868,2012,2074,2156,2228,

%U 2252,2314,2348,2372,2468,2588,2612,2708,2732,2972,3092,3188,3308,3428,3452,3548

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

%C Includes 4*p for primes p with p == 17 or 23 (mod 30). - _Robert Israel_, May 11 2021

%H Robert Israel, <a href="/A023164/b023164.txt">Table of n, a(n) for n = 1..2000</a>

%p fpp:= n -> mpow(n-1, n)[2, 2]:

%p M:= <<0, 1>|<1, 1>>:

%p mpow:= proc(n, p)

%p   if n = 0 then <<1, 0>|<0, 1>>

%p   elif n::even then procname(n/2, p)^2 mod p

%p   else  procname((n-1)/2, p)^2 . M mod p

%p   fi

%p end proc:

%p select(t -> fpp(t)+3 mod t = 0, [$1..10000]); # _Robert Israel_, May 11 2021

%t Select[Range[3600],Mod[Fibonacci[#]+3,#]==0&] (* _Harvey P. Dale_, Sep 21 2021 *)

%Y Cf. A000045, A002708.

%K nonn

%O 1,2

%A _David W. Wilson_

%E Definition clarified by _N. J. A. Sloane_, Sep 21 2021