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

1, 2, 8, 68, 92, 188, 212, 332, 428, 452, 548, 668, 692, 788, 908, 932, 1028, 1052, 1172, 1268, 1292, 1388, 1412, 1508, 1532, 1772, 1868, 2012, 2074, 2156, 2228, 2252, 2314, 2348, 2372, 2468, 2588, 2612, 2708, 2732, 2972, 3092, 3188, 3308, 3428, 3452, 3548

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

Includes 4*p for primes p with p == 17 or 23 (mod 30). - Robert Israel, May 11 2021

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000045, A002708.

Programs

Maple

fpp:= n -> mpow(n-1, n)[2, 2]:
M:= <<0, 1>|<1, 1>>:
mpow:= proc(n, p)
  if n = 0 then <<1, 0>|<0, 1>>
  elif n::even then procname(n/2, p)^2 mod p
  else  procname((n-1)/2, p)^2 . M mod p
  fi
end proc:
select(t -> fpp(t)+3 mod t = 0, [$1..10000]); # Robert Israel, May 11 2021

Mathematica

Select[Range[3600],Mod[Fibonacci[#]+3,#]==0&] (* Harvey P. Dale, Sep 21 2021 *)

Extensions

Definition clarified by N. J. A. Sloane, Sep 21 2021