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A028257 Engel expansion of sqrt(3). 6
1, 2, 3, 3, 6, 17, 23, 25, 27, 73, 84, 201, 750, 24981, 46882, 119318, 121154, 242807, 276226, 3009377, 3383197, 37871208, 45930966, 261728403, 281868388, 3021299588, 3230725884, 13646315477 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

T. D. Noe, Table of n, a(n) for n = 1..300

Naoki Sato, Home page

Eric Weisstein's World of Mathematics, Engel Expansion

Index entries for sequences related to Egyptian fractions

FORMULA

For a number x (here sqrt(3)), define a(1) <= a(2) <= a(3) <= ... so that x = 1/a(1) + 1/(a(1)a(2)) + 1/(a(1)a(2)a(3)) + ... by x(1)=x, a(n) = ceiling(1/x(n)), x(n+1) = x(n)a(n)-1.

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]]; EngelExp[N[3^(1/2), 7! ], 50] (* Vladimir Joseph Stephan Orlovsky, Jun 08 2009 *)

CROSSREFS

Cf. A006784 (for definition of Engel expansion).

Sequence in context: A173094 A087989 A103356 * A100228 A111003 A289277

Adjacent sequences:  A028254 A028255 A028256 * A028258 A028259 A028260

KEYWORD

nonn

AUTHOR

Naoki Sato (naoki(AT)math.toronto.edu)

EXTENSIONS

Better name and more terms from Simon Plouffe

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)