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A225954 A primitive sequence of order n = 2 generated by f(x) = x^2 - (4*x + 13) over Z/(3*5) (see below). 1

%I #39 Feb 10 2018 09:55:30

%S 1,0,13,7,2,9,2,5,1,9,4,13,14,0,2,8,13,6,13,10,14,6,11,2,1,0,13,7,2,9,

%T 2,5,1,9,4,13,14,0,2,8,13,6,13,10,14,6,11,2,1,0,13,7,2,9,2,5,1,9,4,13,

%U 14,0,2,8,13,6,13,10,14,6,11,2,1,0,13,7,2,9,2

%N A primitive sequence of order n = 2 generated by f(x) = x^2 - (4*x + 13) over Z/(3*5) (see below).

%C Z/(3*5) is the integer residue ring modulo 15 with odd prime numbers 3 and 5.

%C Periodic with period 24.

%C The numbers 3 and 12 do not occur in the sequence.

%H Michael De Vlieger, <a href="/A225954/b225954.txt">Table of n, a(n) for n = 0..10000</a>

%H Hong Xu and Wen-Feng Qi, <a href="http://arxiv.org/abs/cs/0601024">Further Results on the Distinctness of Decimations of l-sequences</a>, arXiv:cs/0601024 [cs.CR], 2006.

%H Qun-Xiong Zheng and Wen-Feng Qi, <a href="https://ia.cr/2010/622">A new result on the distinctness of primitive sequences over Z/(pq) modulo 2</a>, IACR, Report 2010/622, 2010.

%H Qun-Xiong Zheng and Wen-Feng Qi, <a href="https://ia.cr/2012/709">Further results on the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers</a>, IACR, Report 2012/709, 2012.

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%t lst = {}; t = 78; AppendTo[lst, {a = 1, b = 0}]; Do[c = Mod[4*b + 13*a, 15]; AppendTo[lst, c]; a = b; b = c, {t - 1}]; Flatten[lst] (* _Arkadiusz Wesolowski_, Jun 01 2013 *)

%t Nest[Append[#, Mod[4 #1 + 13 #2, 15] & @@ {Last@#, #[[-2]]}] &, {1, 0}, 77] (* _Michael De Vlieger_, Feb 10 2018 *)

%o (PARI) lista(nn) = {a = 1; b = 0; print1(a, ", ", b, ", "); for (x=1, nn, nb = (4*b + 13*a) % 15; print1(nb, ", "); a = b; b = nb;);} \\ _Michel Marcus_, Jun 01 2013

%K easy,nonn

%O 0,3

%A _Arkadiusz Wesolowski_, May 21 2013

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