A092340 Prime numbers n such that n^2+2*n divides (Fibonacci(n^2) + Fibonacci(2*n)).

7, 17, 107, 137, 197, 227, 347, 617, 827, 857, 1277, 1427, 1487, 1607, 1667, 1697, 1787, 1877, 1997, 2027, 2087, 2237, 2267, 2657, 2687, 2707, 3167, 3257, 3467, 3527, 3557, 3767, 3917, 4127, 4157, 4217, 4337, 4517, 4547, 4637, 4787, 4967, 5417, 5477

Offset

1,1

Comments

First disagrees with A181605 at n=26: this sequence contains 2707, but A181605 doesn't. Is this a supersequence of A181605? - Nathaniel Johnston, Jun 25 2011

See link for proof of this. - Robert Israel, Apr 13 2021

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 182 terms from Robert G. Wilson v)

Robert Israel, Proof that A181605 is a subsequence of A092340

Maple

filter:= proc(n)
  local M, A;
  uses LinearAlgebra:-Modular;
  if not isprime(n) then return false fi;
  M:= Matrix(2, 2, <<0, 1>|<1, 1>>, datatype=integer);
  A:= MatrixPower(n, M, n^2) + MatrixPower(n, M, 2*n);
  if A[1, 2] mod n <> 0 then return false fi;
  A:= MatrixPower(n+2, M, n^2) + MatrixPower(n+2, M, 2*n);
  A[1, 2] mod (n+2) = 0
end proc:
select(filter, [seq(i, i=3..10000, 2)]); # Robert Israel, Apr 13 2021

Mathematica

fQ[n_] := Mod[ Fibonacci[n^2] + Fibonacci[2 n], n^2 + 2 n] == 0; Select[ Prime@ Range@ 744, fQ] (* Robert G. Wilson v, Nov 07 2010 *)

Prog

(PARI) forprime (i=1, 2000, if(Mod(fibonacci(i^2)+fibonacci(2*i), i^2+2*i)==0, print1(i, ", ")))

Crossrefs

Cf. A000045.

Cf. A181605. - Robert G. Wilson v, Nov 07 2010

Sequence in context: A239150 A092057 A082738 * A181605 A284209 A068172

Adjacent sequences: A092337 A092338 A092339 * A092341 A092342 A092343

Keyword

nonn

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 18 2004

Extensions

Offset changed from 0 to 1 by Robert G. Wilson v, Nov 07 2010

More terms from Robert G. Wilson v, Nov 07 2010

Status

approved