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.

A245599 Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.

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%I A245599 #28 Apr 25 2020 09:58:02
%S A245599 1,11,91,731,5851,46811,374491,2995931,23967451,191739611,1533916891,
%T A245599 12271335131,98170681051,785365448411,6282923587291,50263388698331,
%U A245599 402107109586651,3216856876693211,25734855013545691,205878840108365531,1647030720866924251,13176245766935394011
%N A245599 Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.
%C A245599 Sequence consists of all numbers with binary representation 1(011)*.
%H A245599 Colin Barker, <a href="/A245599/b245599.txt">Table of n, a(n) for n = 1..1001</a>
%H A245599 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9,-8).
%F A245599 a(n) = 1(011)^(n-1) in binary representation.
%F A245599 a(n) = (5*8^n - 12)/28. - _Giovanni Resta_, Apr 25 2020
%F A245599 From _Colin Barker_, Apr 25 2020: (Start)
%F A245599 G.f.: x*(1 + 2*x) / ((1 - x)*(1 - 8*x)).
%F A245599 a(n) = 9*a(n-1) - 8*a(n-2) for n>2.
%F A245599 (End)
%e A245599 A030101(11) = 13,  A030109(11) = 6, and 13 XOR 6 = (1101)_2 XOR (0110)_2 = (1011)_2 = 11, so 11 is in the sequence.
%t A245599 a[n_] := (5*8^n - 12)/28; Array[a, 20] (* _Giovanni Resta_, Apr 25 2020 *)
%o A245599 (PARI) Vec(x*(1 + 2*x) / ((1 - x)*(1 - 8*x)) + O(x^20)) \\ _Colin Barker_, Apr 25 2020
%Y A245599 Cf. A007088, A030109, A030101.
%K A245599 nonn,base,easy
%O A245599 1,2
%A A245599 _Reinhard Muehlfeld_, Jul 27 2014
%E A245599 More terms from _Giovanni Resta_, Apr 25 2020