OFFSET
1,3
COMMENTS
The series 1 + 1/4 + 1/9 + ... converges to (Pi^2)/6, so that a(n) is the least k for which the k-th partial sum exceeds (n-1)/n of the total sum.
Does A177151 have only one run of length 3?
EXAMPLE
a(5)=3 because 1 + 1/4 < 4*T/5 < 1 + 1/4 + 1/9, where T=(Pi^2)/6.
MATHEMATICA
Table[Ceiling[FindArgMin[{k, HarmonicNumber[k, 2] > Pi^2 (n - 1)/(6 n) && k > 0}, k][[1]]], {n, 74}] (* Eric W. Weisstein, Apr 17 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 03 2010
EXTENSIONS
a(2) corrected by Eric W. Weisstein, Apr 17 2018
STATUS
approved