A241505 Composite integers k satisfying F_k-(k/5) == 0 (mod k), where F_k is the k-th Fibonacci number and (k/5) is the Kronecker symbol.

25, 60, 120, 125, 180, 240, 300, 323, 360, 377, 480, 540, 600, 625, 660, 720, 840, 900, 960, 1080, 1200, 1320, 1440, 1500, 1620, 1680, 1800, 1860, 1891, 1920, 1980, 2160, 2400, 2460, 2520, 2640, 2700, 2760, 2880, 3000, 3060, 3125, 3240, 3300, 3360, 3420

Offset

1,1

Comments

Sequence resembles A090820, although they are not identical.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Z. H. Sun and Z. W. Sun, Fibonacci numbers and Fermat's last theorem, Acta Arithmetica 60(4) (1992), 371-388.

Mathematica

Select[Range[2, 5000], ! PrimeQ[#] && Mod[Fibonacci[# - JacobiSymbol[#, 5]], #] == 0 &] (* Jean-François Alcover, Apr 24 2014 *)

Prog

(PARI) forcomposite(n=2, 1e4, if(Mod(fibonacci(n-kronecker(n, 5)), n)==0, print1(n, ", ")))

Crossrefs

Cf. A000045, A090820.

Sequence in context: A250191 A163654 A063317 * A090820 A044127 A044508

Adjacent sequences: A241502 A241503 A241504 * A241506 A241507 A241508

Keyword

nonn

Author

Felix Fröhlich, Apr 24 2014

Status

approved