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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
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OFFSET
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1,1
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COMMENTS
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In this approximate cubing, suggested by T. D. Noe, the 4th iteration yields an integer. Fractions are 4/3, 8/3, 64/3, followed by integers 9728, 920599396352, etc.
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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.
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MATHEMATICA
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NestList[# Ceiling[#^2]&, 4/3, 6]//Numerator (* Harvey P. Dale, Mar 23 2019 *)
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CROSSREFS
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KEYWORD
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easy,frac,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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