A213908 Minimal number of terms in the series 1/n + 1/(n+1) + 1/(n+2) + ... to obtain a sum >= 1.

1, 3, 5, 7, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 31, 32, 34, 36, 37, 39, 41, 43, 44, 46, 48, 49, 51, 53, 55, 56, 58, 60, 62, 63, 65, 67, 68, 70, 72, 74, 75, 77, 79, 80, 82, 84, 86, 87, 89, 91, 92, 94, 96, 98, 99, 101, 103, 104, 106, 108, 110

Offset: 1

Author

Franz Vrabec, Jun 24 2012

Keywords

• nonn

Examples

			a(3)=5 because 1/3 + 1/4 + 1/5 + 1/6 < 1 (4 terms), but 1/3 + 1/4 + 1/5 + 1/6 + 1/7 >= 1 (5 terms).
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Programs

Mathematica

i = 0; s = 0; Table[While[s < 1, i++; s = s + 1/i]; s = s - 1/n; i - n + 1, {n, 100}] (* T. D. Noe, Jun 26 2012 *)
With[{nn=100},Table[Position[Accumulate[1/Range[n,2 nn]],?(#>=1&),1,1],{n,nn}]]//Flatten (* _Harvey P. Dale, May 09 2021 *)

Formula

a(n) = A103762(n) - n + 1. - T. D. Noe, Jun 26 2012