A214966 Array T(m,n) = greatest k such that 1/n + ... + 1/(n+k-1) <= m, by rising antidiagonals.

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

Author

Clark Kimberling, Sep 01 2012

Keywords

• nonn
• tabl

Comments

Row 1: A136617.

Column 1: A115515 = -1 + A002387.

Examples

			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
		

Links

• Clark Kimberling, Rising antidiagonals n = 1..60, flattened

Crossrefs

Cf. A136617, A115515, A002387.

Programs

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 *)