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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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)

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Last modified February 22 18:24 EST 2020. Contains 332148 sequences. (Running on oeis4.)