A168214 Least k such that Sum_{i=n..k} 1/i >= n.

1, 11, 51, 192, 669, 2222, 7135, 22374, 68916, 209348, 628916, 1872269, 5531641, 16238866, 47410139, 137758585, 398617683, 1149205715, 3302324374, 9461757569, 27038402095, 77082571383, 219276117983, 622541323482, 1764242459656

Offset: 1

Author

Zhining Yang, Nov 20 2009

Keywords

• easy
• nice
• nonn

Examples

			1/2 + 1/3 + ... + 1/10 < 2, but 1/2 + 1/3 + ... + 1/11 >= 2, so a(2) = 11.
		

Links

• Northwolves, Harmonic number sum

Crossrefs

Cf. A004080, A002387

Programs

Mathematica

a[n_] := k /. FindRoot[Sum[1/i, {i, n, k}] == n, {k, n*E^n}, WorkingPrecision -> 32] // Ceiling; Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Jun 08 2013 *)

PARI

a(n)=my(k=n,s);while((s+=1./k)Charles R Greathouse IV, Jun 17 2013

VBA

Sub Harmonic_number_sum()
Dim s As Double, i As Long, j As Long, n As Long
For n = 1 To 15
  s = 0
  For i = n To 1000000000
    s = s + 1 / i
    If s >= n Then Exit For
  Next
Debug.Print "a(" & n & ")=" & i:
Next
End Sub

Extensions

a(18)-a(25) from Donovan Johnson, Jun 19 2010

Example edited by Jon E. Schoenfield, Dec 20 2014