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%I #21 Sep 08 2022 08:45:17
%S 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,
%T 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,
%U 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
%N Fibonacci sequence (mod 13).
%H Vincenzo Librandi, <a href="/A105994/b105994.txt">Table of n, a(n) for n = 0..1000</a>
%H Keith Johnson, and Kira Scheibelhut, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.123.4.338">Rational Polynomials That Take Integer Values at the Fibonacci Numbers</a>, American Mathematical Monthly 123.4 (2016): 338-346. See p. 343.
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,-1,0,1,1,-1,-1,1,1,-1,-1,0,1,0,-1,0,1).
%e Sequence is periodic with Pisano period 28.
%t Table[Mod[Fibonacci[n], 13], {n, 0, 100}](* _Vincenzo Librandi_, Feb 04 2014 *)
%t 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 *)
%o (Magma) [Fibonacci(n) mod 13: n in [0..100]]; // _Vincenzo Librandi_, Feb 04 2014
%o (PARI) a(n) = fibonacci(n) % 13; \\ _Michel Marcus_, Oct 01 2017
%Y Cf. A000045.
%K nonn,easy
%O 0,4
%A _Shyam Sunder Gupta_, May 05 2005
%E a(0)=0 prepended by _Vincenzo Librandi_, Feb 04 2014
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