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A140076
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Pierce expansion of the cube root of 1/2.
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0
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1, 4, 5, 7, 8, 18, 384, 7958, 14304, 16623, 18610, 20685, 72923, 883177, 1516692, 2493788, 2504069, 22881179, 110219466, 2241255405, 34982468090, 64356019489, 110512265214, 1142808349967, 3550630472116, 5238523454726, 7129035664265
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 2^(-1/3) = 1-1/4(1-1/5(1-1/7(1-1/8(1-1/18(1-1/384(...))))))
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LINKS
| G. P. Michon, Pierce Expansions.
Eric Weisstein's World of Mathematics, Pierce Expansion.
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FORMULA
| Starting with x(1)=2^(-1/3), a(n) = floor(1/x(n)) and x(n+1) = 1-a(n)x(n).
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EXAMPLE
| a(1) is 1 because the floor of 2^(1/3) is 1.
a(2)=4 because 1/(1-2^(-1/3)) is 4.8473221...
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MATHEMATICA
| $MaxExtraPrecision = 80; x[1] = 2^(-1/3); a[n_] := a[n] = Floor[1/x[n]]; x[n_] := x[n] = 1 - a[n-1]*x[n-1]; Table[a[n], {n, 1, 27}] (* From Jean-François Alcover, Dec 12 2011 *)
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CROSSREFS
| Cf. A091831, A006283, A006284, A061233, A118242.
Sequence in context: A047492 A023629 A033164 * A135186 A011336 A094328
Adjacent sequences: A140073 A140074 A140075 * A140077 A140078 A140079
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Gerard P. Michon (g.michon(AT)att.net), Jun 01 2008
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