

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

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



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



