A023163 Numbers k such that Fibonacci(k) == -2 (mod k).

1, 9, 39, 111, 129, 159, 201, 249, 321, 471, 489, 519, 591, 681, 831, 849, 879, 921, 951, 1041, 1119, 1191, 1329, 1401, 1569, 1641, 1671, 1689, 1761, 1839, 1929, 1959, 2031, 2049, 2199, 2271, 2319, 2361, 2391, 2481, 2559, 2631, 2649, 2721, 2841, 2991, 3039

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..1000

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(p -> fpp(p)+2 mod p = 0, [1, seq(i, i=3..10000, 3)]); # Robert Israel, Feb 01 2017

Mathematica

Join[{1}, Position[Mod[Fibonacci[#], #]-#& /@ Range[10000], -2] // Flatten] (* Jean-François Alcover, Jun 09 2020 *)

Prog

(PARI) isok(k) = Mod(fibonacci(k), k) == -2; \\ Michel Marcus, Jun 09 2020

Crossrefs

Cf. A000045.

Sequence in context: A281381 A226449 A299280 * A054121 A139594 A034263

Adjacent sequences: A023160 A023161 A023162 * A023164 A023165 A023166

Keyword

nonn

Author

David W. Wilson

Status

approved