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Search: id:A065622
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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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+0
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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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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Harry J. Smith, Table of n, a(n) for n=0,...,200
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n) = 4^n*(1+floor[(3/2)^n])-3^n-6^n = A005061(n)-A002380(n)*A000079(n) = A000302(n)*(1+A002379(n))-A000244(n)-A000400(n).
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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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PROGRAM
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(PARI) { for (n=0, 200, a=numerator(1 - (3/4)^n - frac((3/2)^n)); write("b065622.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 24 2009]
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CROSSREFS
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Denominator is A000302. Cf. A002804.
Sequence in context: A001150 A108554 A014376 this_sequence A140421 A114317 A081299
Adjacent sequences: A065619 A065620 A065621 this_sequence A065623 A065624 A065625
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KEYWORD
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frac,sign
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Dec 03 2001
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