A111796 Positive integers sorted by rote weight (A062537) and omega (A001221).

1, 2, 3, 4, 5, 7, 8, 9, 16, 6, 11, 13, 17, 19, 23, 25, 27, 32, 49, 53, 64, 81, 128, 256, 512, 65536, 10, 12, 14, 18

Offset: 1

Author

Jon Awbrey, Sep 01 2005

Keywords

• nonn
• tabf

Comments

Positive integers m sorted by g(m) = A062537(m) and w(m) = A001221(m).

Defining the "wayage" of a rooted tree to be its root degree, the rote corresponding to the positive integer m has a wayage of w(m) = omega(m) = A001221(m).

Examples

			Table of Integers, Primal Codes, Sort Parameters and Subtotals
` ` a ` code` ` | g w | s | t
----------------+-----+---+---
` ` 1 = { } ` ` | 0 0 | 1 | 1
----------------+-----+---+---
` ` 2 = 1:1 ` ` | 1 1 | 1 | 1
----------------+-----+---+---
` ` 3 = 2:1 ` ` | 2 1 | ` |
` ` 4 = 1:2 ` ` | 2 1 | 2 | 2
----------------+-----+---+---
` ` 5 = 3:1 ` ` | 3 1 | ` |
` ` 7 = 4:1 ` ` | 3 1 | ` |
` ` 8 = 1:3 ` ` | 3 1 | ` |
` ` 9 = 2:2 ` ` | 3 1 | ` |
` `16 = 1:4 ` ` | 3 1 | 5 |
----------------+-----+---+---
` ` 6 = 1:1 2:1 | 3 2 | 1 | 6
----------------+-----+---+---
` `11 = 5:1 ` ` | 4 1 | ` |
` `13 = 6:1 ` ` | 4 1 | ` |
` `17 = 7:1 ` ` | 4 1 | ` |
` `19 = 8:1 ` ` | 4 1 | ` |
` `23 = 9:1 ` ` | 4 1 | ` |
` `25 = 3:2 ` ` | 4 1 | ` |
` `27 = 2:3 ` ` | 4 1 | ` |
` `32 = 1:5 ` ` | 4 1 | ` |
` `49 = 4:2 ` ` | 4 1 | ` |
` `53 = 16:1` ` | 4 1 | ` |
` `64 = 1:6 ` ` | 4 1 | ` |
` `81 = 2:4 ` ` | 4 1 | ` |
` 128 = 1:7 ` ` | 4 1 | ` |
` 256 = 1:8 ` ` | 4 1 | ` |
` 512 = 1:9 ` ` | 4 1 | ` |
65536 = 1:16` ` | 4 1 |16 |
----------------+-----+---+---
` `10 = 1:1 3:1 | 4 2 | ` |
` `12 = 1:2 2:1 | 4 2 | ` |
` `14 = 1:1 4:1 | 4 2 | ` |
` `18 = 1:1 2:2 | 4 2 | 4 |20
----------------+-----+---+---
a = this sequence
g = rote weight in gammas = A062537
w = rote wayage in gammas = A001221
s = count in (g, w) class = A111797
t = count in weight class = A061396
		

Links

• J. Awbrey, Riffs and Rotes

Crossrefs

Cf. A001221, A061396, A062504, A062537, A062860.

Cf. A111797, A111798, A111800.