|
%I #5 Dec 04 2016 19:46:30
%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 diagonals.
%C Row 1: A136617
%C Col 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^m/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
|
