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Greatest number k such that A000009(k) <= n.
1

%I #9 Mar 01 2014 19:41:29

%S 2,4,5,6,7,8,8,9,9,10,10,11,11,11,12,12,12,13,13,13,13,14,14,14,14,14,

%T 15,15,15,15,15,16,16,16,16,16,16,17,17,17,17,17,17,17,17,18,18,18,18,

%U 18,18,18,18,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22

%N Greatest number k such that A000009(k) <= n.

%C Inverse of A000009, the sequence of "restricted" partitions (partitions of integers into distinct parts).

%H Jean-François Alcover, <a href="/A238461/b238461.txt">Table of n, a(n) for n = 1..1000</a>

%e q(12) = 15, therefore a(15) = 12.

%t a[n_] := For[k = 1, True, k++, If[PartitionsQ[k] > n, Return[k-1]]]; Table[a[n], {n, 100}]

%Y Cf. A000009, A000041, A198194.

%K nonn

%O 1,1

%A _Jean-François Alcover_, Feb 27 2014