%I #7 Dec 26 2016 05:50:34
%S 9,59,258,1621,41718,163096,18032586,372522402,4134015746,32288273026,
%T 351014976193,4870192684354,16888414224772,69504582263701,
%U 605288885084501,142251062156316087,465610991052284457,1483900314571047497,5622121203907195494,23213137436116662167
%N Engel expansion of 1/e in the base Pi.
%H G. C. Greubel, <a href="/A280103/b280103.txt">Table of n, a(n) for n = 0..250</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PierceExpansion.html">Pierce Expansion</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Engel_expansion">Engel Expansion</a>
%t EngelExp[A_, n_] := Join[Array[Pi &, Floor[A]], First@Transpose@
%t NestList[{Ceiling[Pi/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/Pi} &, {Ceiling[Pi/(A - Floor[A])], (A - Floor[A])/Pi}, n - 1]]; EngelExp[N[1/E, 7!], 20]
%Y Cf. A232325, A280102.
%K nonn
%O 0,1
%A _G. C. Greubel_, Dec 25 2016
|