A226189 Least positive integer k such that 1 + 1/2 + ... + 1/k >= sqrt(n).

1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 18, 21, 24, 27, 31, 35, 39, 44, 49, 55, 61, 68, 75, 83, 92, 101, 112, 122, 134, 147, 161, 175, 191, 208, 227, 246, 267, 289, 313, 339, 366, 396, 427, 460, 495, 533, 573, 616, 661, 709, 760, 815, 872, 934, 998, 1067, 1140

Offset: 1

Author

Clark Kimberling, May 30 2013

Keywords

• nonn

Examples

			a(12) = 18 because 1 + 1/2 + ... + 1/17 < sqrt(12) < 1 + 1/2 + ... + 1/18.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..150

Crossrefs

Cf. A226183, A226190.

Programs

Mathematica

z = 80; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= Sqrt[n] &], {n, 1, z}]; m = Map[a, Range[z]]
Table[Ceiling[x /. FindInstance[HarmonicNumber[x] == Sqrt[n] && x > 0, x][[1]]], {n, 80}] (* Vladimir Reshetnikov, Aug 06 2019 *)