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A065622
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Numerator of 1 - (3/4)^n - frac((3/2)^n), where frac(x) = x - floor(x).
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1
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0, -1, 3, 13, 159, 173, 1767, 12789, 17759, 126237, 292183, 1930245, 3724303, 23940141, 14206087, 99585429, 640559295, 12562430525, 7042526903, 43417422885, 813747135599, 494896655693, 3000760993767, 18098709141429, 249612172740383
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OFFSET
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0,3
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COMMENTS
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The presumption that the fraction is positive for n > 1 underlies the presumed solution to Waring's problem.
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LINKS
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FORMULA
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EXAMPLE
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a(3) = 13 since 1 - (3/4)^3 - frac((3/2)^3)) = 1 - 27/64 - frac(27/8) = 1 - 27/64 - 3/8 = (64 - 27 - 24)/64 = 13/64.
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MATHEMATICA
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Table[1 - (3/4)^n - FractionalPart[(3/2)^n], {n, 0, 24}] // Numerator (* Jean-François Alcover, Apr 26 2016 *)
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PROG
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(PARI) { for (n=0, 200, a=numerator(1 - (3/4)^n - frac((3/2)^n)); write("b065622.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 24 2009
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CROSSREFS
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KEYWORD
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frac,sign
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AUTHOR
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STATUS
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approved
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