cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A011727 A binary m-sequence: expansion of reciprocal of x^14 + x^12 + x^11 + x + 1 (mod 2, shifted by 13 initial 0's).

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%I A011727 #19 Feb 22 2018 16:33:49
%S A011727 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,
%T A011727 0,0,1,0,1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0,0,
%U A011727 1,1,0,1,0,1,1,0,1,0,0,0,0
%N A011727 A binary m-sequence: expansion of reciprocal of x^14 + x^12 + x^11 + x + 1 (mod 2, shifted by 13 initial 0's).
%C A011727 Sequence is 16383-periodic. - _Ray Chandler_, Dec 10 2016
%D A011727 S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.
%D A011727 H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.
%D A011727 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
%H A011727 Ray Chandler, <a href="/A011727/b011727.txt">Table of n, a(n) for n = 0..17000</a>
%H A011727 <a href="/index/Rec#order_16383">Index entries for linear recurrences with constant coefficients</a>, order 16383.
%F A011727 G.f. = x^13/(x^14 + x^12 + x^11 + x + 1) over GF(2). - _M. F. Hasler_, Feb 17 2018
%t A011727 Mod[#, 2] & /@ CoefficientList[Series[x^13/(x^14 + x^12 + x^11 + x + 1), {x, 0, 105}], x] (* _Michael De Vlieger_, Feb 21 2018 *)
%o A011727 (PARI) A011727_vec(N)=Vec(lift(Mod(1,2)/(x^14+x^12+x^11+x+1)+O(x^(N-13))),-N) \\ _M. F. Hasler_, Feb 17 2018
%Y A011727 Cf. A011655..A011745 for other binary m-sequences, and A011746..A011751 for similar expansions over GF(2).
%K A011727 nonn
%O A011727 0,1
%A A011727 _N. J. A. Sloane_