%I #23 Apr 13 2018 11:24:27

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,232,238,428,1103,

%T 3261,6085,15565,20674,43910,177426,193017,1480418,1739984,2573921,

%U 5238757,14403086,25953812,34670065,84077823,258624998,330484686

%N Engel expansion of e^Pi = 23.14069... .

%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="/A059196/b059196.txt">Table of n, a(n) for n = 1..1023</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[E^Pi, 7!], 100] (* _G. C. Greubel_, Dec 28 2016 *)

%Y Cf. A039661.

%K nonn,easy,nice

%O 1,24

%A _Mitch Harris_