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A028254 Engel expansion of sqrt(2). 7
1, 3, 5, 5, 16, 18, 78, 102, 120, 144, 251, 363, 1402, 31169, 88630, 184655, 259252, 298770, 4196070, 38538874, 616984563, 1975413035, 5345718057, 27843871197, 54516286513, 334398528974, 445879679626 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For a number x (here sqrt(2)), 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.

LINKS

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

Benoît Rittaud, La porte d’harmonie — Images des Mathématiques, CNRS, 2009.

Naoki Sato, Home page

Eric Weisstein's World of Mathematics, Engel Expansion

Eric Weisstein's World of Mathematics, Pythagoras's Constant

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[2^(1/2), 7! ], 47] (* Vladimir Joseph Stephan Orlovsky, Jun 08 2009 *)

CROSSREFS

Cf. A006784 (for definition of Engel expansion).

Sequence in context: A188345 A028265 A084041 * A137780 A079372 A055382

Adjacent sequences:  A028251 A028252 A028253 * A028255 A028256 A028257

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

More terms from Simon Plouffe, Jan 05 2002

STATUS

approved

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Last modified December 18 16:24 EST 2017. Contains 296177 sequences.