A105994 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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 *)