A214966 - OEIS

%I #9 Jul 06 2024 19:04:52

%S 1,3,2,10,9,4,30,29,16,6,82,81,48,22,7,226,225,134,67,28,9,615,614,

%T 370,188,86,35,11,1673,1672,1012,517,241,105,41,12,4549,4548,2756,

%U 1413,664,295,124,47,14,12366,12365,7498,3847,1814,811,348,143,54

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

%C Row 1: A136617.

%C Column 1: A115515 = -1 + A002387.

%H Clark Kimberling, <a href="/A214966/b214966.txt">Rising antidiagonals n = 1..60, flattened</a>

%e Northwest corner (the array is read by northeast antidiagonals):

%e     1     2     4     6     7     9

%e     3     9    16    22    28    35

%e    10    29    48    67    86   105

%e    30    81   134   188   241   295

%e    82   225   370   517   664   811

%e   226   614  1012  1413  1814  2216

%t 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 TableForm[t]

%t u = Flatten[Table[t[[i - j]][[j]], {i, 2, 12}, {j, 1, i - 1}]]

%t (* _Peter J. C. Moses_, Aug 29 2012 *)

%Y Cf. A136617, A115515, A002387.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Sep 01 2012