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Search: id:A117636
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| A117636 |
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Start with x=4/3; repeatedly apply the map x -> x ceiling(x^2); sequence gives numerators of the resulting sequence of fractions. |
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+0
1
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| 4, 8, 64, 622592, 8938147991781376, 319561958091941778923367121813504
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In this approximate cubing, suggested by T. D. Noe, the 5th iteration yields an integer. See also A117620 (Start with x=4/3; repeatedly apply the map x -> (x^2) ceiling(x); sequence gives numerators of the resulting sequence of fractions). Fractions are 4/3, 8/3, 64/3, 622592/3, 8938147991781376/1, 319561958091941778923367121813504/3.
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LINKS
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J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
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EXAMPLE
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a(2) = 8, the numerator of (4/3) * ceiling ((4/3)^2) = (4/3) * 2 = 8/3.
a(3) = 64, the numerator of (8/3) * ceiling ((8/3)^2) = (8/3) * 8 = 64/3.
a(4) = X, the numerator of (64/3) * ceiling ((64/3)^2) = (64/3) * 456 = 622592/3.
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CROSSREFS
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Cf. A072340, A085276, A117596, A117620.
Sequence in context: A091095 A075787 A086891 this_sequence A051226 A013112 A068208
Adjacent sequences: A117633 A117634 A117635 this_sequence A117637 A117638 A117639
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 08 2006
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