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 1-7 of 7 results.

A111792 Positive integers sorted by rote weight (A062537) and rote height (A109301).

Original entry on oeis.org

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

Views

Author

Jon Awbrey, Aug 25 2005, revised Aug 27 2005

Keywords

Examples

			Table of Integers, Primal Codes, Sort Parameters and Subtotals
` ` a ` code` ` | g h | s | t
----------------+-----+---+---
` ` 1 = { } ` ` | 0 0 | 1 | 1
----------------+-----+---+---
` ` 2 = 1:1 ` ` | 1 1 | 1 | 1
----------------+-----+---+---
` ` 3 = 2:1 ` ` | 2 2 | ` |
` ` 4 = 1:2 ` ` | 2 2 | 2 | 2
----------------+-----+---+---
` ` 6 = 1:1 2:1 | 3 2 | ` |
` ` 9 = 2:2 ` ` | 3 2 | 2 |
----------------+-----+---+---
` ` 5 = 3:1 ` ` | 3 3 | ` |
` ` 7 = 4:1 ` ` | 3 3 | ` |
` ` 8 = 1:3 ` ` | 3 3 | ` |
` `16 = 1:4 ` ` | 3 3 | 4 | 6
----------------+-----+---+---
` `12 = 1:2 2:1 | 4 2 | ` |
` `18 = 1:1 2:2 | 4 2 | 2 |
----------------+-----+---+---
` `10 = 1:1 3:1 | 4 3 | ` |
` `13 = 6:1 ` ` | 4 3 | ` |
` `14 = 1:1 4:1 | 4 3 | ` |
` `23 = 9:1 ` ` | 4 3 | ` |
` `25 = 3:2 ` ` | 4 3 | ` |
` `27 = 2:3 ` ` | 4 3 | ` |
` `49 = 4:2 ` ` | 4 3 | ` |
` `64 = 1:6 ` ` | 4 3 | ` |
` `81 = 2:4 ` ` | 4 3 | ` |
` 512 = 1:9 ` ` | 4 3 |10 |
----------------+-----+---+---
` `11 = 5:1 ` ` | 4 4 | ` |
` `17 = 7:1 ` ` | 4 4 | ` |
` `19 = 8:1 ` ` | 4 4 | ` |
` `32 = 1:5 ` ` | 4 4 | ` |
` `53 = 16:1` ` | 4 4 | ` |
` 128 = 1:7 ` ` | 4 4 | ` |
` 256 = 1:8 ` ` | 4 4 | ` |
65536 = 1:16` ` | 4 4 | 8 |20
----------------+-----+---+---
a = this sequence
g = rote weight in gammas = A062537
h = rote height in gammas = A109301
s = count in (g, h) class = A111793
t = count in weight class = A061396

Links

Crossrefs

Cf. A007097, A050924, A061396, A062504, A062537, A062860.
Cf. A109300, A109301, A111791, A111793, A111800.

A112095 Positive integers sorted by rote weight, rote height and rote wayage.

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 5, 7, 8, 16, 12, 18, 13, 23, 25, 27, 49, 64, 81, 512, 10, 14, 11, 17, 19, 32, 53, 128, 256, 65536, 36, 37, 61, 125, 169, 343, 529, 625, 729, 2401, 4096, 19683, 262144, 15, 20, 21, 24, 26, 28, 46, 48, 50, 54, 98, 162, 29, 41, 43, 83, 97, 103, 121, 227
Offset: 1

Views

Author

Jon Awbrey, Sep 08 2005, corrected Oct 11 2005

Keywords

Comments

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

Examples

			Table of Primal Functions, Codes, Sort Parameters and Subtotals
================================================================
Primal Function | ` ` ` Primal Code ` = ` a | g h w | r | s | t
================================================================
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 0 | 1 | 1 | 1
================================================================
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 1 | 1 | 1 | 1
================================================================
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 2 1 | ` | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 2 1 | 2 | 2 | 2
================================================================
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 2 1 | 1 | ` |
----------------+---------------------------+-------+---+---+---
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 2 2 | 1 | 2 |
----------------+---------------------------+-------+---+---+---
3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 3 1 | ` | ` |
4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 3 1 | ` | ` |
1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 3 1 | ` | ` |
1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 3 1 | 4 | 4 | 6
================================================================
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 2 2 | ` | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 2 2 | 2 | 2 |
----------------+---------------------------+-------+---+---+---
6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 3 1 | ` | ` |
9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 3 1 | ` | ` |
3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 3 1 | ` | ` |
2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 3 1 | ` | ` |
4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 3 1 | ` | ` |
1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 3 1 | ` | ` |
2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 3 1 | ` | ` |
1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 3 1 | 8 | ` |
----------------+---------------------------+-------+---+---+---
1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 3 2 | ` | ` |
1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 3 2 | 2 |10 |
----------------+---------------------------+-------+---+---+---
5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 4 1 | ` | ` |
7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 4 1 | ` | ` |
8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 4 1 | ` | ` |
1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 4 1 | ` | ` |
16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 4 1 | ` | ` |
1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 4 1 | ` | ` |
1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 4 1 | ` | ` |
1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 4 1 | 8 | 8 |20
================================================================
1:2 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `36 | 5 2 2 | 1 | 1 |
----------------+---------------------------+-------+---+---+---
12:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `37 | 5 3 1 | ` | ` |
18:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `61 | 5 3 1 | ` | ` |
3:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 125 | 5 3 1 | ` | ` |
6:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 169 | 5 3 1 | ` | ` |
4:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 343 | 5 3 1 | ` | ` |
9:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 529 | 5 3 1 | ` | ` |
3:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 625 | 5 3 1 | ` | ` |
2:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 729 | 5 3 1 | ` | ` |
4:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2401 | 5 3 1 | ` | ` |
1:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `4096 | 5 3 1 | ` | ` |
2:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 19683 | 5 3 1 | ` | ` |
1:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `262144 | 5 3 1 |12 | ` |
----------------+---------------------------+-------+---+---+---
2:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `15 | 5 3 2 | ` | ` |
1:2 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `20 | 5 3 2 | ` | ` |
2:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `21 | 5 3 2 | ` | ` |
1:3 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `24 | 5 3 2 | ` | ` |
1:1 6:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `26 | 5 3 2 | ` | ` |
1:2 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `28 | 5 3 2 | ` | ` |
1:1 9:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `46 | 5 3 2 | ` | ` |
1:4 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `48 | 5 3 2 | ` | ` |
1:1 3:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `50 | 5 3 2 | ` | ` |
1:1 2:3 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `54 | 5 3 2 | ` | ` |
1:1 4:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `98 | 5 3 2 | ` | ` |
1:1 2:4 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 162 | 5 3 2 |12 |24 |
----------------+---------------------------+-------+---+---+---
10:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `29 | 5 4 1 | ` | ` |
13:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `41 | 5 4 1 | ` | ` |
14:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `43 | 5 4 1 | ` | ` |
23:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `83 | 5 4 1 | ` | ` |
25:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `97 | 5 4 1 | ` | ` |
27:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 103 | 5 4 1 | ` | ` |
5:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 121 | 5 4 1 | ` | ` |
49:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 227 | 5 4 1 | ` | ` |
2:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 243 | 5 4 1 | ` | ` |
7:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 289 | 5 4 1 | ` | ` |
64:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 311 | 5 4 1 | ` | ` |
8:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 361 | 5 4 1 | ` | ` |
81:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 419 | 5 4 1 | ` | ` |
1:10` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `1024 | 5 4 1 | ` | ` |
2:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2187 | 5 4 1 | ` | ` |
16:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2809 | 5 4 1 | ` | ` |
512:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `3671 | 5 4 1 | ` | ` |
2:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `6561 | 5 4 1 | ` | ` |
1:13` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `8192 | 5 4 1 | ` | ` |
1:14` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 16384 | 5 4 1 | ` | ` |
1:23` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` 8388608 | 5 4 1 | ` | ` |
1:25` ` ` ` ` ` | ` ` ` ` ` ` ` ` `33554432 | 5 4 1 | ` | ` |
2:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` `43046721 | 5 4 1 | ` | ` |
1:27` ` ` ` ` ` | ` ` ` ` ` ` ` ` 134217728 | 5 4 1 | ` | ` |
1:49` ` ` ` ` ` | ` ` ` ` ` 562949953421312 | 5 4 1 | ` | ` |
1:64` ` ` ` ` ` | ` ` `18446744073709551616 | 5 4 1 | ` | ` |
1:81` ` ` ` ` ` | 2417851639229258349412352 | 5 4 1 | ` | ` |
1:512 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^512 | 5 4 1 |28 | ` |
----------------+---------------------------+-------+---+---+---
1:1 5:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `22 | 5 4 2 | ` | ` |
1:1 7:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `34 | 5 4 2 | ` | ` |
1:1 8:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `38 | 5 4 2 | ` | ` |
1:1 16:1` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 106 | 5 4 2 | 4 |32 |
----------------+---------------------------+-------+---+---+---
11:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `31 | 5 5 1 | ` | ` |
17:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `59 | 5 5 1 | ` | ` |
19:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `67 | 5 5 1 | ` | ` |
32:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 131 | 5 5 1 | ` | ` |
53:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 241 | 5 5 1 | ` | ` |
128:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 719 | 5 5 1 | ` | ` |
256:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `1619 | 5 5 1 | ` | ` |
1:11` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2048 | 5 5 1 | ` | ` |
1:17` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `131072 | 5 5 1 | ` | ` |
1:19` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `524288 | 5 5 1 | ` | ` |
65536:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` `821641 | 5 5 1 | ` | ` |
1:32` ` ` ` ` ` | ` ` ` ` ` ` ` `4294967296 | 5 5 1 | ` | ` |
1:53` ` ` ` ` ` | ` ` ` ` `9007199254740992 | 5 5 1 | ` | ` |
1:128 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^128 | 5 5 1 | ` | ` |
1:256 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^256 | 5 5 1 | ` | ` |
1:65536 ` ` ` ` | ` ` ` ` ` ` ` ` ` 2^65536 | 5 5 1 |16 |16 |73
================================================================
a = this sequence
g = rote weight in gammas = A062537
h = rote height in gammas = A109301
w = rote wayage in gammas = A001221
r = number in (g,h,w) set = A112096
s = count in (g, h) class = A111793
t = count in weight class = A061396

Links

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860, A106177.
Cf. A109300, A109301, A111791 to A111800, A112096.

A113197 Positive integers sorted by rote weight, rote height and rote quench.

Original entry on oeis.org

1, 2, 3, 4, 6, 9, 5, 7, 8, 16, 12, 18, 10, 14, 13, 23, 25, 27, 49, 64, 81, 512, 11, 17, 19, 32, 53, 128, 256, 65536, 36, 26, 46, 50, 54, 98, 125, 162, 2401, 15, 21, 37, 61, 169, 343, 529, 625, 729, 4096, 19683, 262144, 20, 24, 28, 48, 22, 34, 38, 106, 29, 41, 43, 83, 97
Offset: 1

Views

Author

Jon Awbrey, Oct 18 2005

Keywords

Comments

For positive integer m, the rote weight in gammas is g(m) = A062537(m), the rote height in gammas is h(m) = A109301(m) and the rote quench or primal code characteristic is q(m) = A108352(m).

Examples

			Primal Functions, Primal Codes, Sort Parameters and Subtotals
================================================================
Primal Function | ` ` ` Primal Code ` = ` a | g h q | r | s | t
================================================================
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 1 | 1 | 1 | 1
================================================================
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 0 | 1 | 1 | 1
================================================================
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 2 2 | ` | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 2 2 | 2 | 2 | 2
================================================================
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 2 0 | ` | ` |
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 2 0 | 2 | 2 |
----------------+---------------------------+-------+---+---+---
3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 3 2 | ` | ` |
4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 3 2 | ` | ` |
1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 3 2 | ` | ` |
1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 3 2 | 4 | 4 | 6
================================================================
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 2 0 | ` | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 2 0 | 2 | 2 |
----------------+---------------------------+-------+---+---+---
1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 3 0 | ` | ` |
1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 3 0 | 2 | ` |
----------------+---------------------------+-------+---+---+---
6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 3 2 | ` | ` |
9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 3 2 | ` | ` |
3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 3 2 | ` | ` |
2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 3 2 | ` | ` |
4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 3 2 | ` | ` |
1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 3 2 | ` | ` |
2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 3 2 | ` | ` |
1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 3 2 | 8 |10 |
----------------+---------------------------+-------+---+---+---
5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 4 2 | ` | ` |
7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 4 2 | ` | ` |
8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 4 2 | ` | ` |
1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 4 2 | ` | ` |
16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 4 2 | ` | ` |
1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 4 2 | ` | ` |
1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 4 2 | ` | ` |
1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 4 2 | 8 | 8 |20
================================================================
a = this sequence
g = rote weight in gammas = A062537
h = rote height in gammas = A109301
q = primal code character = A108352
r = number in (g,h,q) set = A113198
s = count in (g, h) class = A111793
t = count in weight class = A061396

Links

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.
Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
Cf. A111791 to A111801, A112846, A112868 to A112871, A113198.

A113198 Tetrahedron T(g, h, q) = number of rotes of weight g, height h, quench q.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 2, 8, 8, 1, 8, 12, 4, 4, 28, 16
Offset: 1

Views

Author

Jon Awbrey, Oct 18 2005

Keywords

Comments

T(g, h, q) = |{m : A062537(m) = g, A109301(m) = h, A108352(m) = q}|.
This is the column that is labeled "r" in the tabulation of A113197.

Examples

			Table T(g, h, q), omitting empty cells, starts out as follows:
--------+------------------------------------------------------------
g\(h,q) | (0,1) ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` | ` ` ` (1,0) ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` ` (2,0) (2,2) ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` (3,0) (3,2) (3,3) ` ` ` ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (4,0) (4,2) ` ` `
` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (5,2)
========+============================================================
0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
2 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
3 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
3 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
4 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 2 ` ` 8 ` ` ` ` ` ` ` ` ` ` ` ` `
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` `
--------+------------------------------------------------------------
5 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` `12 ` ` 4 ` ` ` ` ` ` ` ` ` `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` `28 ` ` ` `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `16 `
--------+------------------------------------------------------------
Row sums = A111793. Horizontal section sums = A061396.

Links

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.
Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
Cf. A111791 to A111801, A112846, A112868 to A112871, A113197.

A111794 Integers whose rote weight and rote height are equal, sorted by the equated value.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 16, 11, 17, 19, 32, 53, 128, 256, 65536, 31, 59, 67, 131, 241, 719, 1619, 2048, 131072, 524288, 821641, 4294967296, 9007199254740992
Offset: 1

Views

Author

Jon Awbrey, Aug 28 2005

Keywords

Comments

The number of integers m whose rote weight, g(m) = A062537(m) and rote height, h(m) = A109301(m), are both equal to j is 2^(j-1) for j > 0 and 1 for j = 0, as enumerated by the main diagonal of the array shown with sequence A111793.

Examples

			Triangle whose j^th row lists the integers m with g(m) = h(m) = j
j | m such that g(m) = h(m) = j
--+-------------------------------------------------------
0 | 1
1 | 2
2 | 3 4
3 | 5 7 8 16
4 | 11 17 19 32 53 128 256 65536
5 | 31 59 67 131 241 719 1619 2048 131072 524288 821641
` | 4294967296 9007199254740992 2^128 2^256 2^65536

Links

Crossrefs

Cf. A007097, A050924, A061396, A062504, A062537, A062860.
Cf. A109300, A109301, A111791, A111792, A111793, A111800.

A111799 Triangle T(h, w) = number of rotes of height h and wayage w.

Original entry on oeis.org

1, 1, 3, 4, 77
Offset: 1

Views

Author

Jon Awbrey, Sep 01 2005 - Sep 02 2005

Keywords

Comments

T(h, w) = |{positive integers m : A109301(m) = h and A001221(m) = w}|.
Let c(h) = 1 for h = 0 and A050924(h) for h > 0. In other words, c(h) is the sequence [1, A050924] = [1,1,2,9,10^9, ...] that begins with 1 and continues with the terms of A050924. Then the number of nonzero entries in row h is c(h) and their sum is A109300(h). See A111798 for definitions and further details.

Examples

			Table T(h, w), omitting zeros, begins as follows:
h\w| 0 ` 1 ` 2 ` 3 ` 4 ` 5 ` 6 ` 7 ` 8 ` 9
---+---------------------------------------
`0 | 1
`1 | ` ` 1
`2 | ` ` 3 ` 4
`3 | ` `77 ` ? ` ? ` ? ` ? ` ? ` ? ` ? ` ?

Links

Crossrefs

Cf. A001221, A007097, A050924, A061396, A062504, A062537, A062860.
Cf. A109300, A109301, A111791, A111792, A111793, A111798, A111800.

A111795 Positive integers whose rote weight and rote height are equal.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 11, 16, 17, 19, 31, 32, 53, 59, 67, 127, 128
Offset: 1

Views

Author

Jon Awbrey, Aug 28 2005

Keywords

Comments

Positive integers m such that A062537(m) = A109301(m).

Examples

			Tables of Rotes and Primal Codes for a(1) to a(9)
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` o-o ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` o-o ` ` o-o ` ` o-o ` o-o ` ` ` o-o
` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` ` | ` ` ` | ` ` | ` ` ` ` | `
` ` ` ` ` ` o-o ` ` o-o ` o-o ` o-o ` ` ` o-o ` o-o ` ` o-o `
` ` ` ` ` ` | ` ` ` | ` ` | ` ` | ` ` ` ` | ` ` | ` ` ` | ` `
` ` ` o-o ` o-o ` o-o ` ` o-o ` o-o ` ` o-o ` ` o-o ` o-o ` `
` ` ` | ` ` | ` ` | ` ` ` | ` ` | ` ` ` | ` ` ` | ` ` | ` ` `
O ` ` O ` ` O ` ` O ` ` ` O ` ` O ` ` ` O ` ` ` O ` ` O ` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
{ } ` 1:1 ` 2:1 ` 1:2 ` ` 3:1 ` 4:1 ` ` 1:3 ` ` 5:1 ` 1:4 ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
1 ` ` 2 ` ` 3 ` ` 4 ` ` ` 5 ` ` 7 ` ` ` 8 ` ` ` 11` ` 16` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

Links

Crossrefs

Cf. A000079, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860.
Cf. A109300, A109301, A111791, A111792, A111793, A111794, A111800.
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.