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A023175 Numbers k such that Fibonacci(k) == 3 (mod k).

%I A023175 #26 Sep 25 2023 08:15:09
%S A023175 1,2,4,76,124,196,244,316,374,436,556,604,724,796,844,916,964,1084,
%T A023175 1324,1396,1516,1636,1684,1756,1768,1804,1996,2164,2284,2404,2476,
%U A023175 2524,2644,2764,2836,2956,3004,3076,3244,3316,3436,3676,3964,4036,4084,4156,4204
%N A023175 Numbers k such that Fibonacci(k) == 3 (mod k).
%C A023175 Among the first 10000 terms, all are even except for 1 and 20017. - _Robert Israel_, Sep 22 2023
%C A023175 Contains k if k == 4 (mod A001175(k)).  In particular, this is the case if k = 4 * p where p is a prime == 1 or 19 (mod 30).  Most terms appear to be of this type, including all but 141 of the first 10000 terms. - _Robert Israel_, Sep 24 2023
%H A023175 Robert Israel, <a href="/A023175/b023175.txt">Table of n, a(n) for n = 1..10000</a>
%p A023175 filter:= proc(n) uses LinearAlgebra:-Modular; local A;
%p A023175   A:= Mod(n, Matrix([[0,1],[1,1]]),integer[]);
%p A023175   MatrixPower(n,A,n)[1,2] - 3 mod n = 0
%p A023175 end proc:
%p A023175 filter(1):= true:
%p A023175 select(filte, [$1..10000]); # _Robert Israel_, Sep 22 2023
%t A023175 Select[Table[{p,Fibonacci[p]},{p,4500}],Mod[Last[#]-3,First[#]]==0&][[All,1]] (* _Harvey P. Dale_, Sep 22 2021 *)
%Y A023175 Cf. A000045, A001175.
%K A023175 nonn
%O A023175 1,2
%A A023175 _David W. Wilson_