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%I #33 Apr 13 2018 11:14:57
%S 1,1,5,6,13,16,16,38,48,58,104,177,263,332,389,4102,4575,5081,9962,
%T 18316,86613,233239,342534,964372,1452850,7037119,7339713,8270361,
%U 12855437,15900982,19211148,1365302354,1565752087,1731612283
%N Engel expansion of sqrt(5) = 2.23606...
%C Cf. A006784 for definition of Engel expansion.
%D F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
%H Simon Plouffe, <a href="/A059176/b059176.txt">Table of n, a(n) for n = 1..883</a>
%H 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 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 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
%t NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]];
%t EngelExp[N[Sqrt[5], 7!], 50] (* modified by _G. C. Greubel_, Dec 26 2016 *)
%Y Cf. A002163.
%Y Cf. A028259. - _R. J. Mathar_, Jan 30 2009
%K nonn,easy,nice
%O 1,3
%A _Mitch Harris_
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