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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Cf. A090820.

Programs

Mathematica

Select[ Range[ 2, 100000 ], ! PrimeQ[ # ] && Mod[ #, 5 ] != 0 && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 & ]

Extensions

Yorinaga gives table up to 707000

More terms from Eric Rowland, Apr 29 2004

Definition corrected by Eric Rowland, Feb 24 2006