%I #29 Apr 13 2018 11:17:38
%S 1,11,12,60,108,139,176,1228,1356,3166,14807,81596,116387,1367315,
%T 4408018,11560054,15330821,448349063,574897948,613663772,636869505,
%U 999446566,3786082000,6911150147,19780703830,25945009665,33227233233,103529753474,118556676397
%N Engel expansion of log(3) = 1.09861... .
%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="/A059181/b059181.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[Log[3], 7!], 100] (* Modified by _G. C. Greubel_, Dec 27 2016 *)
%Y Cf. A002391.
%K nonn,easy,nice
%O 1,2
%A _Mitch Harris_