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A092340
Prime numbers n such that n^2+2*n divides (Fibonacci(n^2) + Fibonacci(2*n)).
3
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)
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
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