A280096 Engel expansion of 1/phi to the base Pi

6, 18, 95, 340, 9492, 133706, 1693729, 104107693, 692068995, 3295399249, 61983607042, 294907287147, 3866887203952, 1457331336561977, 13487103824303426, 2733476358186221751, 10531585738509590966, 622459086032261357787, 13355793438644297530372, 210369234254618733763935

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Eric Weisstein's World of Mathematics, Pierce Expansion

Wikipedia, Engel Expansion

Example

1/phi = Pi/6 + Pi^2/(6*18) + Pi^3/(6*18*95) + ...

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[2/(1 + Sqrt[5]), 7!], 20]

Crossrefs

Cf. A232325.

Sequence in context: A216727 A174075 A151470 * A009573 A052655 A274499

Adjacent sequences: A280093 A280094 A280095 * A280097 A280098 A280099

Keyword

nonn

Author

G. C. Greubel, Dec 25 2016

Status

approved