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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
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 (list; graph; refs; listen; history; text; internal format)
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
Hong Xu and Wen-Feng Qi, Further Results on the Distinctness of Decimations of l-sequences, arXiv:cs/0601024 [cs.CR], 2006.
Qun-Xiong Zheng and Wen-Feng Qi, A new result on the distinctness of primitive sequences over Z/(pq) modulo 2, IACR, Report 2010/622, 2010.
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified October 2 02:58 EDT 2023. Contains 365831 sequences. (Running on oeis4.)