OFFSET
0,1
COMMENTS
The Mathematica code provided calculates (1+ sqrt(5))/4 and yields the Engel expansion (1+sqrt(5))/4 = Pi/4 + Pi^2/(4*105) + O(Pi^6). Multiplying this expansion by 2 gives this sequence.
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
phi = Pi/2 + Pi^2/(2*105) + Pi^3/(2*105*617) + ...
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 + Sqrt[5])/4, 7!], 20]
CROSSREFS
KEYWORD
nonn
AUTHOR
G. C. Greubel, Dec 25 2016
STATUS
approved