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

Author

Shyam Sunder Gupta, May 05 2005

Keywords

• nonn
• easy

Examples

			Sequence is periodic with Pisano period 28.
		

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).

Crossrefs

Cf. A000045.

Programs

Magma

[Fibonacci(n) mod 13: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014

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 *)

PARI

a(n) = fibonacci(n) % 13; \\ Michel Marcus, Oct 01 2017

Extensions

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