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

1,2

Links

Table of n, a(n) for n=1..25.

Northwolves, Harmonic number sum

Example

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

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 *)

Prog

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

Crossrefs

Cf. A004080, A002387

Sequence in context: A051843 A107464 A027942 * A321421 A317021 A199895

Adjacent sequences: A168211 A168212 A168213 * A168215 A168216 A168217

Keyword

easy,nice,nonn

Author

Zhining Yang, Nov 20 2009

Extensions

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

Example edited by Jon E. Schoenfield, Dec 20 2014

Status

approved