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

Author

G. C. Greubel, Dec 25 2016

Keywords

• nonn

Examples

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

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.

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