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 1-5 of 5 results.

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

Original entry on oeis.org

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

Views

Author

Jon Awbrey, Oct 13 2005

Keywords

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

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.
Cf. A108352, A108353, A108370 to A108374, A111801, A112869.

A112871 Triangle T(h, q) = number of rotes of height h and quench q.

Original entry on oeis.org

1, 1, 5, 2
Offset: 1

Views

Author

Jon Awbrey, Oct 14 2005

Keywords

Comments

T(h, q) = |{positive integers m : A109301(m) = h and A108352(m) = q}|.
This is the column that is labeled "s" in the tabulation of A112870.
q(m) = quench(m) = A108352(m) = primal code characteristic of m.

Examples

			Table T(h, q), omitting empty cells, begins as follows:
h\q| 0 ` 1 ` 2
---+----------
`0 | ` ` 1 ` `
`1 | 1 ` ` ` `
`2 | 5 ` ` ` 2
Row sums = A109300.

Links

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.
Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
Cf. A111791 to A111801, A112846, A112868, A112869, A112870.

Extensions

Too short to be interesting - hope more terms can be supplied soon! - N. J. A. Sloane

A112870 Positive integers sorted by rote height and primal code characteristic.

Original entry on oeis.org

1, 2, 6, 9, 12, 18, 36, 3, 4
Offset: 1

Views

Author

Jon Awbrey, Oct 14 2005

Keywords

Comments

Positive integers m sorted by h(m) = A109301(m) and q(m) = A108352(m).
Using "quench" as a shorter substitute for "primal code characteristic", the rote corresponding to the positive integer m has a quench of q(m) = A108352(m). Numbers with primal code characteristic 0 are "unquenchable".

Examples

			Primal Function | Primal Code = a | h q | s | t
----------------+-----------------+-----+---+---
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` 1 | 0 1 | 1 | 1
----------------+-----------------+-----+---+---
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` 2 | 1 0 | 1 | 1
----------------+-----------------+-----+---+---
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` 6 | 2 0 | ` |
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` 9 | 2 0 | ` |
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` `12 | 2 0 | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` `18 | 2 0 | ` |
1:2 2:2 ` ` ` ` | ` ` ` ` ` ` `36 | 2 0 | 5 |
----------------+-----------------+-----+---+---
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` 3 | 2 2 | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` 4 | 2 2 | 2 | 7
----------------+-----------------+-----+---+---
a = this sequence
h = rote height in gammas = A109301
q = primal code character = A108352
s = count in (h, q) class = A112871
t = count in height class = A109300

Links

Crossrefs

Cf. A061396, A062504, A062537, A062860, A106177, A106178.
Cf. A108352, A108353, A108370 to A108374, A109300, A109301.
Cf. A111791 to A111801, A112846, A112868, A112869, A112871.

A113199 Positive integers sorted by rote weight, rote quench and rote height.

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, 22, 34, 38, 106, 15, 21, 37, 61, 169, 343, 529, 625, 729, 4096, 19683, 262144, 29, 41, 43, 83, 97, 103, 121, 227
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 quench or primal code characteristic is q(m) = A108352(m) and the rote height in gammas is h(m) = A109301(m).
This sequence begins to differ from A113197 at the 40th term, a(40) = 22.

Examples

			Primal Functions, Primal Codes, Sort Parameters and Subtotals
================================================================
Primal Function | ` ` ` Primal Code ` = ` a | g q h | r | s | t
================================================================
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 1 0 | 1 | 1 | 1
================================================================
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 0 1 | 1 | 1 | 1
================================================================
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 2 2 | ` | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 2 2 | 2 | 2 | 2
================================================================
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 0 2 | ` | ` |
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 0 2 | 2 | 2 |
----------------+---------------------------+-------+---+---+---
3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 2 3 | ` | ` |
4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 2 3 | ` | ` |
1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 2 3 | ` | ` |
1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 2 3 | 4 | 4 | 6
================================================================
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 0 2 | ` | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 0 2 | 2 | ` |
----------------+---------------------------+-------+---+---+---
1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 0 3 | ` | ` |
1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 0 3 | 2 | 4 |
----------------+---------------------------+-------+---+---+---
6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 2 3 | ` | ` |
9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 2 3 | ` | ` |
3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 2 3 | ` | ` |
2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 2 3 | ` | ` |
4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 2 3 | ` | ` |
1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 2 3 | ` | ` |
2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 2 3 | ` | ` |
1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 2 3 | 8 | ` |
----------------+---------------------------+-------+---+---+---
5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 2 4 | ` | ` |
7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 2 4 | ` | ` |
8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 2 4 | ` | ` |
1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 2 4 | ` | ` |
16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 2 4 | ` | ` |
1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 2 4 | ` | ` |
1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 2 4 | ` | ` |
1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 2 4 | 8 |16 |20
================================================================
a = this sequence
g = rote weight in gammas = A062537
q = primal code character = A108352
h = rote height in gammas = A109301
r = number in (g,q,h) set = A113200
s = count in (g, q) class = A112869
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, A112868, A112869, A112870, A112871.
Cf. A113197, A113198, A113200.

A113200 Tetrahedron T(g, q, h) = number of rotes of weight g, quench q, height h.

Original entry on oeis.org

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

Views

Author

Jon Awbrey, Oct 18 2005

Keywords

Comments

T(g, q, h) = |{m : A062537(m) = g, A108352(m) = q, A109301(m) = h}|.
This is the column that is labeled "r" in the tabulation of A113199.
a(n) is a permutation of the elements in A113198.

Examples

			Table T(g, q, h), omitting empty cells, starts out as follows:
--------+------------------------------------------------------------
g\(q,h) | (1,0) (0,1) (0,2) ` ` ` (0,3) ` ` ` ` ` ` (0,4) ` ` ` ` ` `
` ` ` ` | ` ` ` ` ` ` ` ` ` (2,2) ` ` ` (2,3) ` ` ` ` ` ` (2,4) (2,5)
` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` (3,3) ` ` ` ` ` ` ` ` `
========+============================================================
0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
2 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
3 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
3 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
4 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` ` ` ` ` ` 8 ` ` ` `
--------+------------------------------------------------------------
5 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` 8 ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `12 ` ` ` ` ` ` ` `28 ` `16 `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` `
--------+------------------------------------------------------------
Row sums = A112869. 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, A112868 to A112871, A113197 to A113199.
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