A183231 -id:A183231 - cp's OEIS frontend

A183232 Second of two complementary trees generated by the triangular numbers. The other tree is A183231.

2, 8, 5, 53, 12, 26, 9, 1538, 63, 103, 17, 404, 33, 64, 14, 1186568, 1593, 2143, 74, 5563, 117, 188, 23, 82619, 432, 628, 41, 2209, 75, 134, 20, 703974775733, 1188108, 1272808, 1649, 2301583, 2208, 2924, 86, 15487393

Offset: 1

Clark Kimberling, Jan 02 2011

See A183231 (first tree).

			First 3 levels:
....................2
...............8...........5
............53...12.....26...9

Cf. A183079, A183231, A183244.

See the formulas at A183231 and A183244.

A183233 Ordering of the numbers in the tree A183231; complement of A183234.

Original entry on oeis.org

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

Clark Kimberling, Jan 02 2011

nonn

Cf. A183231, A183232, A183234.

  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]

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.

A183420 First of two complementary trees generated by the squares; the other tree is A183421.

Original entry on oeis.org

2, 14, 4, 254, 18, 34, 6, 65534, 270, 398, 22, 1294, 40, 62, 9, 4294967294, 65790, 73982, 286, 159998, 418, 574, 27, 1679614, 1330, 1762, 46, 4094, 70, 119, 12

Offset: 1

Clark Kimberling, Jan 04 2011

Begin with the main tree A183169 generated by the squares:
......................1
......................2
...........4.....................3
.......16.......6...........9..........5
...256...20...36..8......81...12....25...7
Every n>2 is in the subtree from 4 or the subtree from 3.  Therefore, on subtracting 2 from all entries of those subtrees, we obtain complementary trees:  A183420 and A183421.

			First three levels:
..................2
.............14.........4
..........254...18....34...6

Cf. A183169, A183420, A183421, A183422, A183231 (analogous trees generated by the triangular numbers).

See the formulas at A183169 and A183422.

cp's OEIS Frontend

A183232 Second of two complementary trees generated by the triangular numbers. The other tree is A183231.

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A183233 Ordering of the numbers in the tree A183231; complement of A183234.

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A183420 First of two complementary trees generated by the squares; the other tree is A183421.

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