A105994 Fibonacci sequence (mod 13).

0, 1, 1, 2, 3, 5, 8, 0, 8, 8, 3, 11, 1, 12, 0, 12, 12, 11, 10, 8, 5, 0, 5, 5, 10, 2, 12, 1, 0, 1, 1, 2, 3, 5, 8, 0, 8, 8, 3, 11, 1, 12, 0, 12, 12, 11, 10, 8, 5, 0, 5, 5, 10, 2, 12, 1, 0, 1, 1, 2, 3, 5, 8, 0, 8, 8, 3, 11, 1, 12, 0, 12, 12, 11, 10, 8, 5, 0, 5, 5, 10, 2, 12, 1, 0, 1, 1, 2, 3, 5, 8, 0, 8, 8

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Keith Johnson, and Kira Scheibelhut, Rational Polynomials That Take Integer Values at the Fibonacci Numbers, American Mathematical Monthly 123.4 (2016): 338-346. See p. 343.

Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,0,1,1,-1,-1,1,1,-1,-1,0,1,0,-1,0,1).

Example

Sequence is periodic with Pisano period 28.

Mathematica

Table[Mod[Fibonacci[n], 13], {n, 0, 100}](* Vincenzo Librandi, Feb 04 2014 *)
PadRight[{}, 120, {0, 1, 1, 2, 3, 5, 8, 0, 8, 8, 3, 11, 1, 12, 0, 12, 12, 11, 10, 8, 5, 0, 5, 5, 10, 2, 12, 1}] (* Harvey P. Dale, Oct 31 2021 *)

Prog

(Magma) [Fibonacci(n) mod 13: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
(PARI) a(n) = fibonacci(n) % 13; \\ Michel Marcus, Oct 01 2017

Crossrefs

Cf. A000045.

Sequence in context: A208361 A145380 A136740 * A120496 A105150 A008963

Adjacent sequences: A105991 A105992 A105993 * A105995 A105996 A105997

Keyword

nonn,easy

Author

Shyam Sunder Gupta, May 05 2005

Extensions

a(0)=0 prepended by Vincenzo Librandi, Feb 04 2014

Status

approved