A227014 a(n) = floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n^5.

1, 10, 104, 543, 1883, 5102, 11717, 23906, 44626, 77735, 128110, 201769, 305989, 449428, 642243, 896212, 1224852, 1643541, 2169636, 2822595, 3624095, 4598154, 5771249, 7172438, 8833478, 10788947, 13076362, 15736301, 18812521, 22352080

Offset: 1

Author

Clark Kimberling, Jul 01 2013

Keywords

• nonn
• easy

Comments

See A227012. It is conjectured that A227014 is a linear recurrence sequence with signature (5,-10,10,-5,1,...Z...,1,-5,-10,-10,-1,0,0), where ...Z... represents a string of 138 zeros; has been confirmed for a(1), a(2),..., a(150000).

Examples

			a(1) = floor(1/(1/1)) = 1.
a(2) = floor(31/(1/2 + 1/3 + ... + 1/32)) = 10.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A227012, A227013.

Programs

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 *)