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

Author

Felix Fröhlich, Apr 24 2014

Keywords

• nonn

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.

Crossrefs

Cf. A000045, A090820.

Programs

Mathematica

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

PARI

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