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%I #28 Apr 13 2018 11:15:17
%S 1,1,1,7,8,12,20,86,94,118,160,179,287,315,22588,49419,66011,80779,
%T 651661,1078390,1093865,4254100,27153191,108815387,220864645,
%U 798937058,992296124,2196903274,17524412379,22828187385
%N Engel expansion of sqrt(10) = 3.16227...
%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 G. C. Greubel, <a href="/A059177/b059177.txt">Table of n, a(n) for n = 1..1000</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[10], 7!], 10] (* modified by _G. C. Greubel_, Dec 26 2016 *)
%Y Cf. A010467.
%K nonn,easy,nice
%O 1,4
%A _Mitch Harris_
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