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

1,2

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).

Links

Table of n, a(n) for n=1..30.

J. Awbrey, Riffs and Rotes

Example

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

Crossrefs

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

Cf. A111797, A111798, A111800.

Sequence in context: A155900 A274949 A107684 * A039124 A335650 A056759

Adjacent sequences: A111793 A111794 A111795 * A111797 A111798 A111799

Keyword

nonn,tabf

Author

Jon Awbrey, Sep 01 2005

Status

approved