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%I #5 Dec 04 2016 19:46:32
%S 1,4,10,22,3,53,35,26,23,20,37,17,48,31,45,73,14,95,67,53,39,64,25,
%T 111,61,97,36,119,83,47,105,58,69,80,91,102,124,146,179,234,322,509,
%U 11,778,448,316,250,206,173,151,140,129,118,107,203,96,181,85,159
%N Least splitter of s(n) and s(n+1), where s(n) = (1 - 1/n)^n.
%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. Since s(n) -> 1/e, the sequence of least splitting rationals also approaches 1/e .
%H Clark Kimberling, <a href="/A227803/b227803.txt">Table of n, a(n) for n = 1..1000</a>
%e The first 15 splitting rationals are 0/1, 1/4, 3/10, 7/22, 1/3, 18/53, 12/35, 9/26, 8/23, 7/20, 13/37, 6/17, 17/48, 11/31, 16/45.
%t z = 100; 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] = (1 - 1/n)^n ; t = Table[r[s[n], s[n + 1]], {n, 1, z}]; Denominator[t] (* A227803, _Peter J. C. Moses_, Jul 15 2013 *)
%Y Cf. A227631, A225594.
%K nonn,frac,easy
%O 1,2
%A _Clark Kimberling_, Jul 31 2013
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