A226187 Least positive integer k such that 1 + 1/2 + ... + 1/k > n/3.
1, 1, 1, 2, 3, 4, 6, 8, 11, 16, 22, 31, 43, 60, 83, 116, 162, 227, 316, 441, 616, 859, 1199, 1674, 2336, 3260, 4550, 6349, 8861, 12367, 17259, 24088, 33617, 46916, 65477, 91380, 127531, 177984, 248397, 346666, 483812, 675214, 942336, 1315136, 1835421, 2561536, 3574912, 4989191, 6962977, 9717617
Offset: 1
Keywords
Examples
a(10) = 16 because 1 + 1/2 + ... + 1/15 < 10/3 < 1 + 1/2 + ... + 1/16.
Programs
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Mathematica
z = 32; f[n_] := 1/n; Do[s = 0; a[n] = NestWhile[# + 1 &, 1, ! (s += f[#]) >= n/3 &], {n, 1, z}]; m = Map[a, Range[z]] -
PARI
a(n)=local(s,k);s=0;k=1;while(s<=n/3,s=s+1/k;k++);k-1
Extensions
More terms from Jean-François Alcover, Jun 05 2013
Deleted obsolete b-file. - N. J. A. Sloane, Jan 04 2019
Comments