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%I #6 Mar 30 2012 18:57:12
%S 1,3,4,6,7,10,11,13,15,16,18,19,21,22,24,25,28,29,31,32,34,36,37,39,
%T 40,42,43,45,46,48,49,51,52,55,56,58,59,61,62,66,67,69,70,72,73,76,78,
%U 79,81,82,84,85,88,89,91,92,94,95,97,98,101,102,105,106,108,109,111,112,115,116,118,120,121,123,124,126,127,130,131,133,136,137,139,140,142,143,146,147,149,151,153,154,156,157,159,160,163,164,166,168,169,171,172,174,175,177,178,181,182,184,186
%N Ordering of the numbers in the tree A183231; complement of A183234.
%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+5n+2)/2 and n+Floor(1/2+sqrt(2n+4)) are in S.
%t nn=200; t={1}; t0=t; While[t=Select[Union[t,(1/2)*(t^2+5t+2), t+Floor[1/2+(2t+4)^(1/2)]], #<=nn &]; t0 !=t, t0=t]; t
%t f[s_List] := Select[ Union@ Join[s, (s^2 + 5 s + 2)/2, s + Floor[1/2 + Sqrt@ (2 s + 4)]], # < 201 &]; NestWhile[f, {1}, UnsameQ, All]
%Y Cf. A183231, A183232, A183234.
%K nonn
%O 1,2
%A _Clark Kimberling_, Jan 02 2011