A241505 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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, ", ")))