A049062 Composite n coprime to 5 such that Fibonacci(n) == Legendre(n,5) (mod n).

4181, 5474, 5777, 6479, 6721, 10877, 12958, 13201, 15251, 17302, 27071, 34561, 40948, 41998, 44099, 47519, 51841, 54839, 64079, 64681, 65471, 67861, 68251, 72831, 75077, 78089, 88198, 90061, 95038, 96049, 97921

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..500

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, 100000 ], ! PrimeQ[ # ] && Mod[ #, 5 ] != 0 && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]

Crossrefs

Cf. A090820.

Sequence in context: A179249 A045734 A155511 * A093372 A212424 A319168

Adjacent sequences: A049059 A049060 A049061 * A049063 A049064 A049065

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Yorinaga gives table up to 707000

More terms from Eric Rowland, Apr 29 2004

Definition corrected by Eric Rowland, Feb 24 2006

Status

approved