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Search: id:A028257
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| A028257 |
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Engel expansion of sqrt(3). |
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+0
5
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| 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; listen)
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OFFSET
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1,2
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LINKS
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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
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FORMULA
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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) = ceil(1/x(n)), x(n+1) = x(n)a(n)-1.
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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[3^(1/2), 7! ], 50] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 08 2009]
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CROSSREFS
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Cf. A006784 (for definition of Engel expansion).
Sequence in context: A049875 A087989 A103356 this_sequence A100228 A111003 A140182
Adjacent sequences: A028254 A028255 A028256 this_sequence A028258 A028259 A028260
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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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Better name and more terms from Simon Plouffe (simon.plouffe(AT)gmail.com).
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