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.

1, 4, 14, 46, 153, 535, 1855, 6449, 22460, 81237

Offset: 1

Author

Ivan Neretin, May 24 2015

Keywords

• nonn
• more

Comments

Presumably, every natural number is reached at some step exactly, rather than "stepped over" (as is the case with harmonic series).

Examples

			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.
		

Crossrefs

Cf. A258252, A004080 (analog for harmonic series), A002387.