A183422 Ordering of the numbers in the tree A183420; complement of A183423.

2, 4, 6, 9, 12, 14, 16, 18, 20, 22, 25, 27, 30, 32, 34, 36, 38, 40, 42, 44, 46, 49, 51, 53, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 81, 83, 85, 87, 90, 92, 94, 96, 100, 102, 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

Offset: 1

Author

Clark Kimberling, Jan 04 2011

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A183423, the complement of A183422.

Programs

Mathematica

 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

Formula

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.