

A225954


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


1



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

0,3


COMMENTS

Z/(3*5) is the integer residue ring modulo 15 with odd prime numbers 3 and 5.
Periodic with period 24.
The numbers 3 and 12 do not occur in the sequence.


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Hong Xu and WenFeng Qi, Further Results on the Distinctness of Decimations of lsequences, arXiv:cs/0601024 [cs.CR], 2006.
QunXiong Zheng and WenFeng Qi, A new result on the distinctness of primitive sequences over Z/(pq) modulo 2, IACR, Report 2010/622, 2010.
QunXiong Zheng and WenFeng Qi, Further results on the distinctness of binary sequences derived from primitive sequences modulo squarefree odd integers, IACR, Report 2012/709, 2012.
Index entries for linear recurrences with constant coefficients, 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).


MATHEMATICA

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 *)
Nest[Append[#, Mod[4 #1 + 13 #2, 15] & @@ {Last@#, #[[2]]}] &, {1, 0}, 77] (* Michael De Vlieger, Feb 10 2018 *)


PROG

(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


CROSSREFS

Sequence in context: A300886 A301496 A078438 * A133723 A324279 A222464
Adjacent sequences: A225951 A225952 A225953 * A225955 A225956 A225957


KEYWORD

easy,nonn


AUTHOR

Arkadiusz Wesolowski, May 21 2013


STATUS

approved



