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%I #6 Dec 04 2016 19:46:32
%S 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,
%T 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,
%U 4,6,1,6,4,3,2,5,3,5,8,1,5,4,3,2,5,3
%N Least splitter of s(n) and s(n+1), where s(n) = sum{(k + 1/2)^(-1/2), k >= 1}.
%C 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.
%H Clark Kimberling, <a href="/A227779/b227779.txt">Table of n, a(n) for n = 1..1000</a>
%e 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.
%t 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 *)
%Y Cf. A227631.
%K nonn,frac,easy
%O 1,2
%A _Clark Kimberling_, Jul 30 2013
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