A227685 Least splitter of s(n) and s(n+1), where s(n) = 1 + 1/2^2 + ... + 1/n^2.

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, 51, 23, 59, 18, 31, 44, 70, 13, 60, 47, 34, 76, 21, 50, 29, 66, 37, 45, 53, 69, 85, 117, 189, 8, 243, 147, 107, 83, 67, 59, 51, 94, 43, 78, 35, 97, 62, 89, 27, 154

Offset: 1

Author

Clark Kimberling, Jul 19 2013

Keywords

• nonn
• frac
• easy

Comments

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.

Examples

			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 < ...
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A227631, A227686.

Programs

Mathematica

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 = Table[r[s[n], s[n + 1]], {n, 1, 150}] (*fractions*)
Denominator[t] (*A227685*)
Numerator[t]   (*A227686*)