This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A227685 #4 Jul 20 2013 14:06:52
%S A227685 1,3,5,7,15,2,19,13,11,9,16,23,7,19,12,29,17,22,32,57,5,88,53,38,28,
%T A227685 51,23,59,18,31,44,70,13,60,47,34,76,21,50,29,66,37,45,53,69,85,117,
%U A227685 189,8,243,147,107,83,67,59,51,94,43,78,35,97,62,89,27,154
%N A227685 Least splitter of s(n) and s(n+1), where s(n) = 1 + 1/2^2 + ... + 1/n^2.
%C A227685 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.
%H A227685 Clark Kimberling, <a href="/A227685/b227685.txt">Table of n, a(n) for n = 1..1000</a>
%e A227685 The denominators (A227685) and numerators (A227686) can be read from this chain: s(1) <= 1 < s(2) < 4/3 < s(3) < 7/5 < s(4) < 10/7 < s(5) < 22/15 < ...
%t A227685 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^(-2), {k, 1, n}]
%t A227685 t = Table[r[s[n], s[n + 1]], {n, 1, 150}] (*fractions*)
%t A227685 Denominator[t] (*A227685*)
%t A227685 Numerator[t] (*A227686*)
%Y A227685 Cf. A227631, A227686.
%K A227685 nonn,frac,easy
%O A227685 1,2
%A A227685 _Clark Kimberling_, Jul 19 2013