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

1,2

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

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 *)

Crossrefs

Cf. A000045, A002708.

Sequence in context: A132219 A226730 A202553 * A053922 A030445 A093990

Adjacent sequences: A023161 A023162 A023163 * A023165 A023166 A023167

Keyword

nonn

Author

David W. Wilson

Extensions

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

Status

approved