%I #25 Apr 13 2018 11:19:00
%S 3,4,5,18,27,37,415,445,1812,2475,3928,6707,14673,65863,89033,265841,
%T 1293955,1525697,2541166,7906280,107955268,154190828,887303031,
%U 1767107652,3068165143,3209500563,92762706640,147991352023
%N Engel expansion of 1/log(10) = 0.434294....
%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="/A059184/b059184.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[1/Log[10], 7!], 100] (* Modified by _G. C. Greubel_, Dec 27 2016 *)
%Y Cf. A002285 (1/log(10)).
%K nonn,easy,nice
%O 1,1
%A _Mitch Harris_