A090820 -id:A090820 - cp's OEIS frontend

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

N. J. A. Sloane

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).

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.

Cf. A090820.

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

Yorinaga gives table up to 707000
More terms from Eric Rowland, Apr 29 2004
Definition corrected by Eric Rowland, Feb 24 2006

A094063 Composite n such that Fibonacci(n) == Legendre(n,5) == -1 (mod n).

Original entry on oeis.org

5777, 10877, 12958, 17302, 40948, 41998, 75077, 88198, 95038, 100127, 113573, 130942, 133742, 156178, 160378, 161027, 162133, 163438, 168838, 203942, 219742, 231703, 300847, 314158, 336598, 390598, 393118, 430127, 467038, 480478, 534508

Offset: 1

Eric Rowland, Apr 29 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..235

Cf. A049062, A090820, A093372.

Select[ Range[ 2, 100000 ], ! PrimeQ[ # ] && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 && JacobiSymbol[ #, 5 ] == -1 & ]

More terms from Ryan Propper, Nov 07 2006

A093372 Composite k such that Fibonacci(k) == Legendre(k,5) == 1 (mod k).

Original entry on oeis.org

4181, 5474, 6479, 6721, 13201, 15251, 27071, 34561, 44099, 47519, 51841, 54839, 64079, 64681, 65471, 67861, 68251, 72831, 78089, 90061, 96049, 97921, 109871, 118441, 139359, 146611, 157079, 163081, 168299, 186961, 196559, 197209, 219781

Offset: 1

N. J. A. Sloane, Apr 29 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..300

Cf. A049062, A090820, A094063.

Select[ Range[ 2, 100000 ], ! PrimeQ[ # ] && Mod[ Fibonacci[ # ] - JacobiSymbol[ #, 5 ], # ] == 0 && JacobiSymbol[ #, 5 ] == 1 & ]

More terms from Eric Rowland, Apr 29 2004

More terms from Ryan Propper, Jul 21 2006

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.

Original entry on oeis.org

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

Felix Fröhlich, Apr 24 2014

nonn

Sequence resembles A090820, although they are not identical.

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.

Cf. A000045, A090820.

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

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

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

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A094063 Composite n such that Fibonacci(n) == Legendre(n,5) == -1 (mod n).

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A093372 Composite k such that Fibonacci(k) == Legendre(k,5) == 1 (mod k).

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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.

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