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 A083683 #35 Oct 08 2022 08:33:47
%S A083683 12,23,45,89,177,353,705,1409,2817,5633,11265,22529,45057,90113,
%T A083683 180225,360449,720897,1441793,2883585,5767169,11534337,23068673,
%U A083683 46137345,92274689,184549377,369098753,738197505,1476395009,2952790017,5905580033,11811160065
%N A083683 a(n) = 11*2^n + 1.
%C A083683 An Engel expansion of 2/11 to the base 2 as defined in A181565, with the associated series expansion 2/11 = 2/12 + 2^2/(12*23) + 2^3/(12*23*45) + 2^4/(12*23*45*89) + ... . - _Peter Bala_, Oct 29 2013
%H A083683 Vincenzo Librandi, <a href="/A083683/b083683.txt">Table of n, a(n) for n = 0..1000</a>
%H A083683 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A083683 a(n) = 2*a(n-1) - 1.
%F A083683 a(n) = 3*a(n-1) - 2*a(n-2), n>1. - _Vincenzo Librandi_, Nov 03 2011
%F A083683 G.f. (12-13*x)/((2*x-1)*(x-1)). - _R. J. Mathar_, Nov 03 2011
%F A083683 E.g.f.: exp(x)*(1 + 11*exp(x)). - _Stefano Spezia_, Oct 08 2022
%t A083683 11*2^Range[0,30]+1 (* or *) LinearRecurrence[{3,-2},{12,23},40] (* _Harvey P. Dale_, Aug 17 2017 *)
%o A083683 (Magma) [11*2^n+1 : n in [0..30]]; // _Vincenzo Librandi_, Nov 03 2011
%o A083683 (PARI) a(n)=11*2^n+1 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y A083683 Cf. A020737, A083575, A083686, A083705, A168596, A181565, A195744.
%K A083683 nonn,easy
%O A083683 0,1
%A A083683 _N. J. A. Sloane_, Jun 15 2003