%I
%S 0,1,2,2,2,5,5,5,5,5,5,5,5,5,14,14,14,14,14,14,14,14,14,14,14,14,14,
%T 14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,42,42,42,42,42,42,42,42,
%U 42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,42
%N a(0) = 0, and for n >=1, a(n) = the largest Catalan number <= n.
%C After n>0, A000108(n) occurs A000245(n) times.
%C For all n>0, a(A000108(n)) = A000108(n) [the first occurrence of the nth Catalan number in this sequence].
%C Minimal i such that A081289(i) >= A081289(n) [the original definition of the sequence].
%C In other words, the first position k in A081289 where A081289(n) occurs (the minimal k such that A081289(k) = A081289(n)), and also the first position k in A081288 where A081288(n) occurs (the minimal k such that A081288(k) = A081288(n)). The starting point of the run which contains the nth term in those sequences.
%F a(0) = 0, a(n) = A000108(A081288(n)1).
%t Join[{0},With[{catnos=Reverse[CatalanNumber[Range[10]]]},Table[ SelectFirst[ catnos,#<=n&],{n,80}]]] (* This program uses the SelectFirst function from Mathematica version 10 *) (* _Harvey P. Dale_, Jul 27 2014 *)
%Y Cf. A000108, A081288, A081289, A072643, A239903.
%K nonn
%O 0,3
%A _Antti Karttunen_, Mar 17 2003
%E Name changed by _Antti Karttunen_, Apr 26 2014
