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A214966
Array T(m,n) = greatest k such that 1/n + ... + 1/(n+k-1) <= m, by rising antidiagonals.
1
1, 3, 2, 10, 9, 4, 30, 29, 16, 6, 82, 81, 48, 22, 7, 226, 225, 134, 67, 28, 9, 615, 614, 370, 188, 86, 35, 11, 1673, 1672, 1012, 517, 241, 105, 41, 12, 4549, 4548, 2756, 1413, 664, 295, 124, 47, 14, 12366, 12365, 7498, 3847, 1814, 811, 348, 143, 54
OFFSET
1,2
COMMENTS
Row 1: A136617.
Column 1: A115515 = -1 + A002387.
EXAMPLE
Northwest corner (the array is read by northeast antidiagonals):
1 2 4 6 7 9
3 9 16 22 28 35
10 29 48 67 86 105
30 81 134 188 241 295
82 225 370 517 664 811
226 614 1012 1413 1814 2216
MATHEMATICA
t = Table[1 + Floor[x /. FindRoot[HarmonicNumber[N[x + z, 150]] - HarmonicNumber[N[z - 1, 150]] == m, {x, Floor[-E^bm/2 + (-1 + E^m) z]}, WorkingPrecision -> 100]], {m, 1, #}, {z, 1, #}] &[12]
TableForm[t]
u = Flatten[Table[t[[i - j]][[j]], {i, 2, 12}, {j, 1, i - 1}]]
(* Peter J. C. Moses, Aug 29 2012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 01 2012
STATUS
approved