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A028254
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Engel expansion of sqrt(2).
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7
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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
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OFFSET
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1,2
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COMMENTS
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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) = ceil(1/x(n)), x(n+1) = x(n)a(n)-1.
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LINKS
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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
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MATHEMATICA
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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] [From Vladimir Joseph Stephan Orlovsky, Jun 08 2009]
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CROSSREFS
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Cf. A006784 (for definition of Engel expansion).
Sequence in context: A188345 A028265 A084041 * A137780 A079372 A055382
Adjacent sequences: A028251 A028252 A028253 * A028255 A028256 A028257
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KEYWORD
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nonn
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AUTHOR
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Naoki Sato (naoki(AT)math.toronto.edu)
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EXTENSIONS
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More terms from Simon Plouffe, Jan 05, 2002
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STATUS
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approved
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