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.

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

Views

Author

Clark Kimberling, Jan 04 2011

Keywords

Comments

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.

Examples

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

Crossrefs

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

Formula

See the formulas at A183169 and A183422.

A183423 Ordering of the numbers in tree A183421; complement of A183422.

Original entry on oeis.org

1, 3, 5, 7, 8, 10, 11, 13, 15, 17, 19, 21, 23, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 98, 99, 101, 103, 105, 107, 108, 109, 111, 113, 115, 117, 118, 120, 122, 124, 126, 128, 129, 131, 133, 135, 137, 139, 140, 142, 143, 145, 147, 149, 151, 152, 154, 155, 157, 159, 161, 163, 164, 166, 167, 168, 170, 172, 174, 176, 177, 179, 180, 181, 183, 185, 187, 189, 190, 192, 193, 195, 197, 199
Offset: 1

Views

Author

Clark Kimberling, Jan 04 2011

Keywords

Examples

			See A183422.

Crossrefs

Cf. A183421, A183422.

Programs

  • Mathematica
     nn=200; t={1}; 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: 1 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.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 04 2011

Keywords

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.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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