cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Clark Kimberling, Jan 02 2011

Keywords

Comments

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.

Examples

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

Crossrefs

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

Formula

See the formulas at A183079 and A183233.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 02 2011

Keywords

Crossrefs

Cf. A183232, A183233.

Programs

  • Mathematica
    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]

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

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

Views

Author

Clark Kimberling, Jan 02 2011

Keywords

Crossrefs

Cf. A183231, A183232, A183234.

Programs

  • 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.
Showing 1-3 of 3 results.

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