%I
%S 2,4,6,9,12,14,16,18,20,22,25,27,30,32,34,36,38,40,42,44,46,49,51,53,
%T 56,58,60,62,64,66,68,70,72,74,76,78,81,83,85,87,90,92,94,96,100,102,
%U 104,106,110,112,114,116,119,121,123,125,127,130,132,134,136,138,141,144,146,148,150,153,156,158,160,162,165,169,171,173,175,178,182,184,186,188,191,194,196,198,200
%N Ordering of the numbers in the tree A183420; complement of A183423.
%F The monotonic ordering of the numbers in the set S generated by these rules: 2 is in S, and if n is in S, then n^2+4*n+2 and n+Floor[1/2+sqrt(n+2)] is in S.
%e The complementary trees A183420 and A183421 contain initial terms (2,14,4,254,18,34,6,...) and (1,7,3,79,10,23,5,...). A183422 comes from arranging in increasing order the numbers in the first tree: (2,4,6,9,,12,14,...), these being complementary to the numbers in the second tree.
%t nn=200; t={2}; t0=t; While[t=Select[Union[t,(t^2+4t+2),t+Floor[1/2+(t+2)^(1/2)]], #<=nn&]; t0 !=t, t0=t]; t
%Y Cf. A183423, the complement of A183422.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 04 2011
