login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A226763
Least k such that 1/k <= mean of {1, 1/2, 1/3, ..., 1/n}.
2
1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16
OFFSET
1,2
LINKS
FORMULA
a(n) = ceiling(n/(Sum_{k=1..n} 1/k)).
EXAMPLE
1/4 < mean{1,1/2,1/3,...,1/9} < 1/3, so that a(9) = 4.
MATHEMATICA
f[n_] := Mean[Table[1/k, {k, 1, n}]]
Table[Floor[1/f[n]], {n, 1, 120}] (* A226762 *)
Table[Ceiling[1/f[n]], {n, 1, 120}] (* this sequence *)
CROSSREFS
Cf. A226762.
Sequence in context: A172263 A337635 A140437 * A050500 A076885 A274024
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 19 2013
EXTENSIONS
Name corrected by Jason Yuen, Nov 02 2024
STATUS
approved