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A112480 Positive integers sorted by rote weight, rote wagage and rote height. 2
1, 2, 3, 4, 9, 5, 7, 8, 16, 6, 13, 23, 25, 27, 49, 64, 81, 512, 11, 17, 19, 32, 53, 128, 256, 65536, 12, 18, 10, 14, 37, 61, 125, 169, 343, 529, 625, 729, 2401, 4096, 19683, 262144, 29, 41, 43, 83, 97, 103, 121, 227, 243, 289, 311, 361, 419, 1024, 2187, 2809, 3671 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For positive integer m, the rote weight in gammas is g(m) = A062537(m), the rote wayage or root degree is w(m) = omega(m) = A001221(m) and the rote height in gammas is h(m) = A109301(m).

LINKS

Table of n, a(n) for n=1..59.

J. Awbrey, Riffs and Rotes

EXAMPLE

Table of Primal Functions, Codes, Sort Parameters and Subtotals

================================================================

Primal Function | ` ` ` Primal Code ` = ` a | g w h | r | s | t

================================================================

{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 0 | 1 | 1 | 1

================================================================

1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 1 | 1 | 1 | 1

================================================================

2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 1 2 | ` | ` |

1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 1 2 | 2 | 2 | 2

================================================================

2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 1 2 | 1 | ` |

----------------+---------------------------+-------+---+---+---

3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 1 3 | ` | ` |

4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 1 3 | ` | ` |

1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 1 3 | ` | ` |

1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 1 3 | 4 | 5 |

----------------+---------------------------+-------+---+---+---

1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 2 2 | 1 | 1 | 6

================================================================

6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 1 3 | ` | ` |

9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 1 3 | ` | ` |

3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 1 3 | ` | ` |

2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 1 3 | ` | ` |

4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 1 3 | ` | ` |

1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 1 3 | ` | ` |

2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 1 3 | ` | ` |

1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 1 3 | 8 | ` |

----------------+---------------------------+-------+---+---+---

5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 1 4 | ` | ` |

7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 1 4 | ` | ` |

8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 1 4 | ` | ` |

1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 1 4 | ` | ` |

16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 1 4 | ` | ` |

1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 1 4 | ` | ` |

1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 1 4 | ` | ` |

1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 1 4 | 8 |16 |

----------------+---------------------------+-------+---+---+---

1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 2 2 | ` | ` |

1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 2 2 | 2 | ` |

----------------+---------------------------+-------+---+---+---

1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 2 3 | ` | ` |

1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 2 3 | 2 | 4 |20

================================================================

12:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `37 | 5 1 3 | ` | ` |

18:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `61 | 5 1 3 | ` | ` |

3:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 125 | 5 1 3 | ` | ` |

6:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 169 | 5 1 3 | ` | ` |

4:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 343 | 5 1 3 | ` | ` |

9:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 529 | 5 1 3 | ` | ` |

3:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 625 | 5 1 3 | ` | ` |

2:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 729 | 5 1 3 | ` | ` |

4:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2401 | 5 1 3 | ` | ` |

1:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `4096 | 5 1 3 | ` | ` |

2:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 19683 | 5 1 3 | ` | ` |

1:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `262144 | 5 1 3 |12 | ` |

----------------+---------------------------+-------+---+---+---

10:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `29 | 5 1 4 | ` | ` |

13:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `41 | 5 1 4 | ` | ` |

14:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `43 | 5 1 4 | ` | ` |

23:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `83 | 5 1 4 | ` | ` |

25:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `97 | 5 1 4 | ` | ` |

27:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 103 | 5 1 4 | ` | ` |

5:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 121 | 5 1 4 | ` | ` |

49:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 227 | 5 1 4 | ` | ` |

2:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 243 | 5 1 4 | ` | ` |

7:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 289 | 5 1 4 | ` | ` |

64:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 311 | 5 1 4 | ` | ` |

8:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 361 | 5 1 4 | ` | ` |

81:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 419 | 5 1 4 | ` | ` |

1:10` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `1024 | 5 1 4 | ` | ` |

2:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2187 | 5 1 4 | ` | ` |

16:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2809 | 5 1 4 | ` | ` |

512:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `3671 | 5 1 4 | ` | ` |

2:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `6561 | 5 1 4 | ` | ` |

1:13` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `8192 | 5 1 4 | ` | ` |

1:14` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 16384 | 5 1 4 | ` | ` |

1:23` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` 8388608 | 5 1 4 | ` | ` |

1:25` ` ` ` ` ` | ` ` ` ` ` ` ` ` `33554432 | 5 1 4 | ` | ` |

2:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` `43046721 | 5 1 4 | ` | ` |

1:27` ` ` ` ` ` | ` ` ` ` ` ` ` ` 134217728 | 5 1 4 | ` | ` |

1:49` ` ` ` ` ` | ` ` ` ` ` 562949953421312 | 5 1 4 | ` | ` |

1:64` ` ` ` ` ` | ` ` `18446744073709551616 | 5 1 4 | ` | ` |

1:81` ` ` ` ` ` | 2417851639229258349412352 | 5 1 4 | ` | ` |

1:512 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^512 | 5 1 4 |28 | ` |

----------------+---------------------------+-------+---+---+---

11:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `31 | 5 1 5 | ` | ` |

17:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `59 | 5 1 5 | ` | ` |

19:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `67 | 5 1 5 | ` | ` |

32:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 131 | 5 1 5 | ` | ` |

53:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 241 | 5 1 5 | ` | ` |

128:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 719 | 5 1 5 | ` | ` |

256:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `1619 | 5 1 5 | ` | ` |

1:11` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2048 | 5 1 5 | ` | ` |

1:17` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `131072 | 5 1 5 | ` | ` |

1:19` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `524288 | 5 1 5 | ` | ` |

65536:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` `821641 | 5 1 5 | ` | ` |

1:32` ` ` ` ` ` | ` ` ` ` ` ` ` `4294967296 | 5 1 5 | ` | ` |

1:53` ` ` ` ` ` | ` ` ` ` `9007199254740992 | 5 1 5 | ` | ` |

1:128 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^128 | 5 1 5 | ` | ` |

1:256 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^256 | 5 1 5 | ` | ` |

1:65536 ` ` ` ` | ` ` ` ` ` ` ` ` ` 2^65536 | 5 1 5 |16 |56 |

----------------+---------------------------+-------+---+---+---

1:2 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `36 | 5 2 2 | 1 | ` |

----------------+---------------------------+-------+---+---+---

2:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `15 | 5 2 3 | ` | ` |

1:2 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `20 | 5 2 3 | ` | ` |

2:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `21 | 5 2 3 | ` | ` |

1:3 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `24 | 5 2 3 | ` | ` |

1:1 6:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `26 | 5 2 3 | ` | ` |

1:2 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `28 | 5 2 3 | ` | ` |

1:1 9:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `46 | 5 2 3 | ` | ` |

1:4 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `48 | 5 2 3 | ` | ` |

1:1 3:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `50 | 5 2 3 | ` | ` |

1:1 2:3 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `54 | 5 2 3 | ` | ` |

1:1 4:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `98 | 5 2 3 | ` | ` |

1:1 2:4 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 162 | 5 2 3 |12 | ` |

----------------+---------------------------+-------+---+---+---

1:1 5:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `22 | 5 2 4 | ` | ` |

1:1 7:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `34 | 5 2 4 | ` | ` |

1:1 8:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `38 | 5 2 4 | ` | ` |

1:1 16:1` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 106 | 5 2 4 | 4 |17 |73

================================================================

a = this sequence

g = rote weight in gammas = A062537

w = rote wayage in gammas = A001221

h = rote height in gammas = A109301

r = number in (g,h,w) set = A112481

s = count in (g, w) class = A111797

t = count in weight class = A061396

CROSSREFS

Cf. A000079, A001221, A007097, A014221, A050924.

Cf. A061396, A062504, A062537, A062860, A106177.

Cf. A109300, A109301, A111791 to A111800.

Cf. A112095, A112096, A112481.

Sequence in context: A303951 A326776 A249746 * A298196 A112095 A260435

Adjacent sequences:  A112477 A112478 A112479 * A112481 A112482 A112483

KEYWORD

nonn,tabf

AUTHOR

Jon Awbrey, Sep 27 2005

STATUS

approved

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Last modified June 23 21:09 EDT 2021. Contains 345402 sequences. (Running on oeis4.)