OFFSET
1,1
COMMENTS
Dottie number = 1/2 + 1/2/3 + 1/2/3/3 + 1/2/3/3/4 + 1/2/3/3/4/5 + 1/2/3/3/4/5/15 +...
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..500
Jean-Christophe Pain, An exact series expansion for the Dottie number, arXiv:2303.17962 [math.NT], 2023.
Eric Weisstein's World of Mathematics, Engel Expansion
Eric Weisstein's World of Mathematics, Dottie Number
MATHEMATICA
EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]} &, {Ceiling[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; z = FindRoot[x == Cos[x], {x, 1}, WorkingPrecision -> 10000][[1, -1]]; EngelExp[z, 30]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ben Branman, May 02 2012
STATUS
approved