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%I #4 Mar 30 2012 18:57:12
%S 1,3,5,7,8,10,11,13,15,17,19,21,23,24,26,28,29,31,33,35,37,39,41,43,
%T 45,47,48,50,52,54,55,57,59,61,63,65,67,69,71,73,75,77,79,80,82,84,86,
%U 88,89,91,93,95,97,98,99,101,103,105,107,108,109,111,113,115,117,118,120,122,124,126,128,129,131,133,135,137,139,140,142,143,145,147,149,151,152,154,155,157,159,161,163,164,166,167,168,170,172,174,176,177,179,180,181,183,185,187,189,190,192,193,195,197,199
%N Ordering of the numbers in tree A183421; complement of A183422.
%F The monotonic ordering of the numbers in the set S generated by these rules: 1 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 See A183422.
%t nn=200; t={1}; 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. A183421, A183422.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 04 2011