OFFSET
1,2
COMMENTS
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..1000
EXAMPLE
a(1) = floor(1/(1/1)) = 1, a(2) = floor(31/(1/2 + 1/3 + ... + 1/32) = 10.
MATHEMATICA
Clear[g]; g[n_] := N[n^5, 100]; a = {1}; Do[AppendTo[a, Floor[(#2 - #1 + 1)/(HarmonicNumber[#2]-HarmonicNumber[#1 - 1])] &[g[k - 1] + 1, g[k]]], {k, 2, 200}]; a (* Peter J. C. Moses, Jul 05 2012 *)
(* confirm generating function *)
p = {1, -4, 5, 9, 54, 117, 117, 122, 118, 122, 118, 122, 118, 122,
118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118,
122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122,
118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118,
122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122,
119, 117, 129, 107, 134, 106, 134, 106, 134, 106, 134, 106, 134,
106, 134, 106, 134, 107, 129, 117, 119, 122, 118, 122, 118, 122,
118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118,
122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122,
118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118,
122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122, 118, 122,
117, 126, 113, 113, 64, 5, 1};
q = {0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 5, -10, 10, -5,
1}; gf = Fold[x #1 + #2 &, 0, p]/Fold[x #1 + #2 &, 0, q]; CoefficientList[Series[Factor[gf], {x, 0, 100}], x] (* Peter J. C. Moses, Jul 08 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 01 2013
STATUS
approved