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A227779
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Least splitter of s(n) and s(n+1), where s(n) = sum{(k + 1/2)^(-1/2), k >= 1}.
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1
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1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 3, 5, 1, 3, 2, 3, 5, 1, 4, 3, 2, 3, 6, 1, 4, 3, 2, 3, 5, 1, 5, 3, 2, 3, 4, 7, 1, 4, 3, 2, 3, 4, 6, 1, 5, 3, 5, 2, 3, 4, 7, 1, 5, 3, 5, 2, 3, 4, 6, 1, 6, 4, 3, 2, 5, 3, 5, 8, 1, 5, 4, 3, 2, 5, 3
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OFFSET
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1,2
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COMMENTS
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Suppose that x < y. The least splitter of x and y is introduced at A227631 as the least positive integer d such that x <= c/d < y for some integer c; the number c/d is called the least splitting rational of x and y. It appears that d=1 (i.e., c/d is an integer) for rationals c/d in positions given by A024206.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..1000
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EXAMPLE
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The first 15 splitting rationals are 1, 3/2, 2, 5/2, 3, 7/2, 11/3, 4, 9/2, 14/3, 5, 16/3, 11/2, 23/4, 6.
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MATHEMATICA
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r[x_, y_] := Module[{c, d}, d = NestWhile[#1 + 1 &, 1, ! (c = Ceiling[#1 x - 1]) < Ceiling[#1 y] - 1 &]; (c + 1)/d]; s[n_] := s[n] = Sum[(k + 1/2)^(-1/2), {k, 1, n}]; t = Table[r[s[n], s[n + 1]], {n, 1, 220}]; Denominator[t] (* Peter J. C. Moses, Jul 15 2013 *)
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CROSSREFS
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Cf. A227631.
Sequence in context: A023118 A122197 A030718 * A194066 A308916 A353171
Adjacent sequences: A227776 A227777 A227778 * A227780 A227781 A227782
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Clark Kimberling, Jul 30 2013
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STATUS
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approved
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