A183233 -id:A183233 - cp's OEIS frontend

A183234 Ordering of the numbers in tree A183232; complement of A183233.

2, 5, 8, 9, 12, 14, 17, 20, 23, 26, 27, 30, 33, 35, 38, 41, 44, 47, 50, 53, 54, 57, 60, 63, 64, 65, 68, 71, 74, 75, 77, 80, 83, 86, 87, 90, 93, 96, 99, 100, 103, 104, 107, 110, 113, 114, 117, 119, 122, 125, 128, 129, 132, 134, 135, 138, 141, 144, 145, 148, 150, 152, 155, 158, 161, 162, 165, 167, 170, 173, 176, 179, 180, 183, 185, 188, 189, 192, 195, 198, 199

Offset: 1

Clark Kimberling, Jan 02 2011

nonn

Cf. A183232, A183233.

nn=200; t={2}; 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, {2}, UnsameQ, All]

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+5n+2)/2 and n+Floor(1/2+sqrt(2n+4)) are in S.

A183231 First of two complementary trees generated by the triangular numbers. The second tree is A183232.

Original entry on oeis.org

1, 4, 3, 19, 7, 13, 6, 229, 25, 43, 11, 118, 18, 34, 10, 26794, 250, 376, 32, 1033, 52, 89, 16, 7258, 133, 208, 24, 664, 42, 76, 15, 359026204, 27025, 31876, 272, 71629, 403, 593, 40, 536128, 1078, 1483, 62, 4184, 102, 169, 22, 26357428

Offset: 1

Clark Kimberling, Jan 02 2011

Begin with the main tree A183079 generated by the triangular numbers:
......................1
......................2
.............3.................4
.........6.......5........10........7
.......21..9...15..8....55..14....28..11
Every n>2 is in the subtree from 3 or the subtree from 4.
Therefore, on subtracting 2 from all entries of those subtrees, we obtain complementary trees:  A183231 and A183232.

			First three levels:
............1
.......4.........3
....19...7.....13..6

Cf. A183079, A183232 (second tree), A183233.

See the formulas at A183079 and A183233.

cp's OEIS Frontend

A183234 Ordering of the numbers in tree A183232; complement of A183233.

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