A280103 Engel expansion of 1/e in the base Pi.

9, 59, 258, 1621, 41718, 163096, 18032586, 372522402, 4134015746, 32288273026, 351014976193, 4870192684354, 16888414224772, 69504582263701, 605288885084501, 142251062156316087, 465610991052284457, 1483900314571047497, 5622121203907195494, 23213137436116662167

Offset: 0

Author

G. C. Greubel, Dec 25 2016

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250
• Eric Weisstein's World of Mathematics, Pierce Expansion
• Wikipedia, Engel Expansion

Crossrefs

Cf. A232325, A280102.

Programs

Mathematica

EngelExp[A_, n_] := Join[Array[Pi &, Floor[A]], First@Transpose@
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]