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A090820 Composite n such that Fibonacci(n) == Legendre(n,5) (mod n). 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A163654 A063317 A241505 * A044127 A044508 A166873
KEYWORD
nonn
AUTHOR
Eric Rowland, Apr 29 2004
EXTENSIONS
More terms from Felix Fröhlich, Apr 24 2014
STATUS
approved

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Last modified April 13 05:19 EDT 2024. Contains 371639 sequences. (Running on oeis4.)