login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A227688
Numerator of least splitting rational of s(n) and s(n+1), where s(n) = 1/sqrt(1) + 1/sqrt(2) + ... + 1/sqrt(n).
3
1, 2, 5, 3, 7, 4, 13, 9, 5, 21, 11, 17, 6, 19, 13, 20, 7, 22, 15, 23, 8, 41, 25, 17, 26, 9, 46, 28, 19, 29, 49, 10, 41, 31, 21, 32, 54, 11, 45, 34, 23, 35, 47, 12, 73, 49, 37, 25, 38, 64, 13, 79, 53, 40, 27, 41, 55, 97, 14, 71, 43, 72, 29, 44, 59, 104, 15
OFFSET
1,2
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.
LINKS
EXAMPLE
The denominators (A227687) and numerators (A227688) can be read from these chains:
1 < 2 < 5/2 < 3 < 7/2 < 4 < 13/3 < 9/2 < 5 < 21/4 < 11/2 < 17/3 < 6 < . . . ;
s(1) <= 1 < s(2) < 2 < s(3) < 5/2 < s(4) < 3 < s(5) < 4 < s(6) < 13/3 < . . .
MATHEMATICA
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), {k, 1, n}]; t = Table[r[s[n], s[n + 1]], {n, 1, 15}] (*fractions*)
fd = Denominator[t] (*A227687*)
fn = Numerator[t] (*A227688*)
CROSSREFS
Sequence in context: A257983 A210770 A338347 * A358923 A328827 A181184
KEYWORD
nonn,frac,easy
AUTHOR
Clark Kimberling, Jul 21 2013
STATUS
approved