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A168214
Least k such that Sum_{i=n..k} 1/i >= n.
0
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
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
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