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

1,2

Comments

Row 1: A136617.

Column 1: A115515 = -1 + A002387.

Links

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

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

Cf. A136617, A115515, A002387.

Sequence in context: A056861 A302846 A214844 * A367300 A103245 A019242

Adjacent sequences: A214963 A214964 A214965 * A214967 A214968 A214969

Keyword

nonn,tabl,changed

Author

Clark Kimberling, Sep 01 2012

Status

approved