A112868 Positive integers sorted by rote weight and primal code characteristic.

1, 2, 3, 4, 6, 9, 5, 7, 8, 16, 10, 12, 14, 18, 11, 13, 17, 19, 23, 25, 27, 32, 49, 53, 64, 81, 128, 256, 512, 65536, 22, 26, 34, 36, 38, 46, 50, 54, 98, 106, 125, 162, 2401, 15, 21, 29, 31, 37, 41, 43, 59, 61, 67, 83, 97, 103, 121, 131, 169, 227, 241, 243, 289, 311, 34, 361

Offset: 1

Author

Jon Awbrey, Oct 13 2005

Keywords

• nonn
• tabf

Comments

Positive integers m sorted by g(m) = A062537(m) and q(m) = A108352(m).

Examples

			Primal Functions, Primal Codes, Sort Parameters, Subtotals
==========================================================
Primal Function | ` ` ` Primal Code ` = ` a | g q | s | t
==========================================================
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 1 | 1 | 1
==========================================================
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 0 | 1 | 1
==========================================================
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 2 | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 2 | 2 | 2
==========================================================
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 0 | ` |
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 0 | 2 |
----------------+---------------------------+-----+---+---
3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 2 | ` |
4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 2 | ` |
1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 2 | ` |
1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 2 | 4 | 6
==========================================================
1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 0 | ` |
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 0 | ` |
1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 0 | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 0 | 4 |
----------------+---------------------------+-----+---+---
5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 2 | ` |
6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 2 | ` |
7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 2 | ` |
8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 2 | ` |
9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 2 | ` |
3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 2 | ` |
2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 2 | ` |
1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 2 | ` |
4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 2 | ` |
16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 2 | ` |
1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 2 | ` |
2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 2 | ` |
1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 2 | ` |
1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 2 | ` |
1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 2 | ` |
1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 2 |16 |20
==========================================================
a = this sequence
g = rote weight in gammas = A062537
q = primal code character = A108352
s = count in (g, q) class = A112869
t = count in weight class = A061396
		

Links

• J. Awbrey, Table for Rote Weights 0 to 5
• J. Awbrey, Riffs and Rotes

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.

Cf. A108352, A108353, A108370 to A108374, A111801, A112869.