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A182503
Engel expansion of the Dottie number, A003957.
4
2, 3, 3, 4, 5, 15, 17, 66, 196, 233, 284, 375, 1613, 2131, 3574, 14122, 24171, 49097, 56871, 69361, 193406, 243145, 289951, 682749, 14501588, 21191773, 121635191, 810759781, 1292785381, 136110231377, 294401497761
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
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
Sequence in context: A372592 A238394 A372595 * A278288 A023154 A358073
KEYWORD
nonn,easy
AUTHOR
Ben Branman, May 02 2012
STATUS
approved