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 A059176 #35 Jun 04 2025 12:47:05
%S A059176 1,1,5,6,13,16,16,38,48,58,104,177,263,332,389,4102,4575,5081,9962,
%T A059176 18316,86613,233239,342534,964372,1452850,7037119,7339713,8270361,
%U A059176 12855437,15900982,19211148,1365302354,1565752087,1731612283
%N A059176 Engel expansion of sqrt(5) = 2.23606...
%C A059176 Cf. A006784 for definition of Engel expansion.
%D A059176 F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
%H A059176 Simon Plouffe, <a href="/A059176/b059176.txt">Table of n, a(n) for n = 1..883</a>
%H A059176 F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbruechen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
%H A059176 P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
%H A059176 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t A059176 EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
%t A059176 NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
%t A059176 EngelExp[N[Sqrt[5], 7!], 50] (* modified by _G. C. Greubel_, Dec 26 2016 *)
%Y A059176 Cf. A002163.
%Y A059176 Essentially the same as A028259.
%K A059176 nonn,easy,nice
%O A059176 1,3
%A A059176 _Mitch Harris_