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 A258255 #10 Aug 17 2015 20:42:30
%S A258255 1,4,14,46,153,535,1855,6449,22460,81237
%N A258255 Least k such that n <= Sum_{i=1..k} 1/A258252(i), where A258252 are the numbers having lowest possible denominators for the sums of reciprocals.
%C A258255 Presumably, every natural number is reached at some step exactly, rather than "stepped over" (as is the case with harmonic series).
%e A258255 For the first few terms of A258252, the sums of their reciprocal are: 1, 3/2, 5/3, 2, 9/4, 7/3, 12/5, 5/2, 18/7, 13/5, 14/5, 17/6, 20/7, 3, ... that are equal to 1, 2, 3 for n=1, 4, 14. So a(1)=1, a(2)=4, a(3)=14.
%Y A258255 Cf. A258252, A004080 (analog for harmonic series), A002387.
%K A258255 nonn,more
%O A258255 1,2
%A A258255 _Ivan Neretin_, May 24 2015