A183233 Ordering of the numbers in the tree A183231; complement of A183234.
1, 3, 4, 6, 7, 10, 11, 13, 15, 16, 18, 19, 21, 22, 24, 25, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 45, 46, 48, 49, 51, 52, 55, 56, 58, 59, 61, 62, 66, 67, 69, 70, 72, 73, 76, 78, 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
Offset: 1
Keywords
Programs
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Mathematica
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 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]
Formula
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.