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 A078689 #23 May 04 2025 01:57:49
%S A078689 1,2,1,1,8,1,1,14,1,1,20,1,1,26,1,1,32,1,1,38,1,1,44,1,1,50,1,1,56,1,
%T A078689 1,62,1,1,68,1,1,74,1,1,80,1,1,86,1,1,92,1,1,98,1,1,104,1,1,110,1,1,
%U A078689 116,1,1,122,1,1,128,1,1,134,1,1,140,1,1,146
%N A078689 Continued fraction expansion of e^(1/3).
%H A078689 Thomas J. Osler, <a href="http://www.jstor.org/stable/27641838">A proof of the continued fraction expansion of e^(1/M)</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 62-66.
%H A078689 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%F A078689 a(3k+1) = 6k+2, otherwise a(i) = 1.
%F A078689 G.f.: -(x^2-x+1)*(x^3-3*x^2-3*x-1) / ((x-1)^2*(x^2+x+1)^2). - _Colin Barker_, Jun 24 2013
%F A078689 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/18 + log(2)/6. - _Amiram Eldar_, May 04 2025
%t A078689 ContinuedFraction[Exp[1/3], 100] (* _Amiram Eldar_, May 20 2022 *)
%Y A078689 Cf. A016933, A058281, A092041.
%K A078689 cofr,nonn,easy
%O A078689 0,2
%A A078689 _Benoit Cloitre_, Dec 17 2002