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%I #24 Apr 13 2018 11:24:51
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,3,8,17,111,236,419,
%T 2475,3741,4123,5563,5622,18000,33641,42744,130605,696987,975174,
%U 1034590,2806140,14026897,14137435,65788323,73121589,229261119
%N Engel expansion of Pi^e = 22.4592.
%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="/A059197/b059197.txt">Table of n, a(n) for n = 1..1022</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[Pi^E, 7!], 100] (* Modified by _G. C. Greubel_, Dec 28 2016 *)
%Y Cf. A059850.
%K nonn,easy,nice
%O 1,23
%A _Mitch Harris_
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