A090820 Composite n such that Fibonacci(n) == Legendre(n,5) (mod n).

25, 60, 120, 125, 180, 240, 300, 360, 480, 540, 600, 625, 660, 720, 840, 900, 960, 1080, 1200, 1320, 1440, 1500, 1620, 1680, 1800, 1860, 1920, 1980, 2160, 2400, 2460, 2520, 2640, 2700, 2760, 2880, 3000, 3060, 3125, 3240, 3300, 3360, 3420, 3600, 3660, 3720

Offset

1,1

Comments

If n is a prime, not 5, then Fibonacci(n) == Legendre(n,5) (mod n) (see for example G. H. Hardy and E. M. Wright, Theory of Numbers).

Links

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

Masataka Yorinaga, On a congruencial property of Fibonacci numbers (numerical experiments), Math. J. Okayama Univ. 19 (1976/77), no. 1, 5-10.

Masataka Yorinaga, On a congruencial property of Fibonacci numbers (considerations and remarks), Math. J. Okayama Univ. 19 (1976/77), no. 1, 11-17.

Mathematica

Select[ Range[ 2, 5000 ], ! PrimeQ[ # ] && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]

Prog

(PARI) N=10^4; for(n=2, N, if(Mod((fibonacci(n)), n)==kronecker(n, 5) && !isprime(n), print1(n, ", ")));

Crossrefs

Cf. A049062, A093372, A094063.

Sequence in context: A163654 A063317 A241505 * A044127 A044508 A166873

Adjacent sequences: A090817 A090818 A090819 * A090821 A090822 A090823

Keyword

nonn

Author

Eric Rowland, Apr 29 2004

Extensions

More terms from Felix Fröhlich, Apr 24 2014

Status

approved