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 A227014 Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n^5. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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). 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 Cf. A227012, A227013. Sequence in context: A015588 A162667 A027270 * A036334 A190954 A163309 Adjacent sequences:  A227011 A227012 A227013 * A227015 A227016 A227017 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 01 2013 STATUS approved

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Last modified April 18 03:59 EDT 2021. Contains 343072 sequences. (Running on oeis4.)