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A280096
Engel expansion of 1/phi to the base Pi
1
6, 18, 95, 340, 9492, 133706, 1693729, 104107693, 692068995, 3295399249, 61983607042, 294907287147, 3866887203952, 1457331336561977, 13487103824303426, 2733476358186221751, 10531585738509590966, 622459086032261357787, 13355793438644297530372, 210369234254618733763935
OFFSET
0,1
LINKS
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
KEYWORD
nonn
AUTHOR
G. C. Greubel, Dec 25 2016
STATUS
approved