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Search: id:A117620
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| A117620 |
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Start with x=4/3; repeatedly apply the map x -> (x^2) ceiling(x); sequence gives numerators of the resulting sequence of fractions. |
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+0
2
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| 4, 32, 4096, 285212672, 3536203627938199896064, 277354671274375905946316289020, 27735467127437590594631628902073909856749798039036448735232
(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, does an iteration eventually yield an integer, after which denominators are 1? Fractions are 4/3, 32/9, 4096/81, 285212672/2187, 3536203627938199896064/1594323, 27735467127437590594631628902073909856749798039036448735232/2541865828329, 8393707510592229745861012598171776416393703955772365464679357805492895042198412632866136478758067686243059846017657263750451410617880163800261945260539460460740608/6461081889226673298932241.
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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(4) = 285212672 because (4096/81)^2 * ceiling(4096/81) = (4096/81)^2 * ceiling(4096/81) = * ceiling(50.5679012) = (16777216/6561) * 51 = 285212672/2187.
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CROSSREFS
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Cf. A072340, A085276, A117596.
Sequence in context: A053005 A012092 A027639 this_sequence A059904 A145645 A042831
Adjacent sequences: A117617 A117618 A117619 this_sequence A117621 A117622 A117623
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 07 2006
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