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.
%I A127961 #25 Mar 18 2025 07:35:16
%S A127961 1,11,1011,101011,10101011,1010101011,101010101011,10101010101011,
%T A127961 1010101010101011,101010101010101011,10101010101010101011,
%U A127961 1010101010101010101011,101010101010101010101011,10101010101010101010101011,1010101010101010101010101011
%N A127961 a(n) = A007583(n) written in binary.
%H A127961 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (101,-100).
%F A127961 From _Colin Barker_, Sep 02 2013: (Start)
%F A127961 a(n) = (89 + 10^(1+2*n))/99.
%F A127961 a(n) = 101*a(n-1) - 100*a(n-2).
%F A127961 G.f.: -(90*x-1)/((x-1)*(100*x-1)). (End)
%F A127961 E.g.f.: exp(x)*(89 + 10*exp(99*x))/99. - _Elmo R. Oliveira_, Mar 16 2025
%e A127961 A007583(2) = 11, which becomes 1011 when written in binary.
%t A127961 Table[FromDigits[IntegerDigits[(2^(2n + 1) + 1)/3, 2]], {n, 0, 14}]
%t A127961 LinearRecurrence[{101,-100},{1,11},20] (* _Harvey P. Dale_, Jul 21 2024 *)
%Y A127961 Cf. A007583.
%K A127961 easy,nonn,less,base
%O A127961 0,2
%A A127961 _Artur Jasinski_, Feb 09 2007
%E A127961 Edited and extended by _Stefan Steinerberger_, Jun 11 2007
%E A127961 More terms from _Colin Barker_, Sep 02 2013