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

%I A214966 #9 Jul 06 2024 19:04:52
%S A214966 1,3,2,10,9,4,30,29,16,6,82,81,48,22,7,226,225,134,67,28,9,615,614,
%T A214966 370,188,86,35,11,1673,1672,1012,517,241,105,41,12,4549,4548,2756,
%U A214966 1413,664,295,124,47,14,12366,12365,7498,3847,1814,811,348,143,54
%N A214966 Array T(m,n) = greatest k such that 1/n + ... + 1/(n+k-1) <= m, by rising antidiagonals.
%C A214966 Row 1: A136617.
%C A214966 Column 1: A115515 = -1 + A002387.
%H A214966 Clark Kimberling, <a href="/A214966/b214966.txt">Rising antidiagonals n = 1..60, flattened</a>
%e A214966 Northwest corner (the array is read by northeast antidiagonals):
%e A214966     1     2     4     6     7     9
%e A214966     3     9    16    22    28    35
%e A214966    10    29    48    67    86   105
%e A214966    30    81   134   188   241   295
%e A214966    82   225   370   517   664   811
%e A214966   226   614  1012  1413  1814  2216
%t A214966 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]
%t A214966 TableForm[t]
%t A214966 u = Flatten[Table[t[[i - j]][[j]], {i, 2, 12}, {j, 1, i - 1}]]
%t A214966 (* _Peter J. C. Moses_, Aug 29 2012 *)
%Y A214966 Cf. A136617, A115515, A002387.
%K A214966 nonn,tabl
%O A214966 1,2
%A A214966 _Clark Kimberling_, Sep 01 2012