A111792 -id:A111792 - cp's OEIS frontend

A111791 Positive integers sorted by rote height, as measured by A109301.

1, 2, 3, 4, 6, 9, 12, 18, 36, 5, 7, 8, 10, 13, 14, 15, 16, 20, 21, 23, 24, 25, 26, 27, 28, 30, 35, 37, 39, 40, 42, 45, 46, 48, 49, 50, 52, 54, 56, 60, 61, 63, 64, 65, 69, 70, 72, 74, 75, 78, 80, 81, 84, 90, 91, 92, 98, 100

Offset: 1

Jon Awbrey, Aug 24 2005, revised Sep 02 2005

			Table in which the h-th row lists the positive integers of rote height h:
h | m such that rhig(m) = A109301(m) = h
--+------------------------------------------------------
0 |  1
--+------------------------------------------------------
1 |  2
--+------------------------------------------------------
2 |  3  4  6  9 12 18 36
--+------------------------------------------------------
3 |  5  7  8 10 13 14 15 16 20 21 23 24 25 26 27  28 30
  | 35 37 39 40 42 45 46 48 49 50 52 54 56 60 61  63
  | 64 65 69 70 72 74 75 78 80 81 84 90 91 92 98 100 ...
--+------------------------------------------------------
4 | 11 17 19 22 29 32 33 34 38 41 43 44 47 51 53 55
  | 57 58 66 68 71 73 76 77 82 83 85 86 87 88 89 94
  | 95 96 97 99 ...
--+------------------------------------------------------
5 | 31 59 62 67 79 93 ...
--+------------------------------------------------------
First column = A007097. Count in h^th row = A109300(h).
Cumulative count up through the h^th row = A050924(h+1).

J. Awbrey, Riffs and Rotes

Cf. A007097, A050924, A061396, A062504, A062537, A062860.

Cf. A109300, A109301, A111792 to A111800.

A111793 Triangle T(g, h) = number of rotes of weight g and height h, both in gammas.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 10, 8, 1, 24, 32, 16

Offset: 1

Jon Awbrey, Aug 26 2005, revised Aug 28 2005

T(g, h) = |{positive integers m : A062537(m) = g and A109301(m) = h}|.
Row sums = A061396. Column sums = A109300. See A111792 for details.
Main diagonal T(j, j) = 2^(j-1) for j > 0, T(0, 0) = 1.

			Table T(g, h), omitting zeros, starts out as follows:
g\h| 0 ` 1 ` 2 ` 3 ` 4 ` 5
---+-----------------------
`0 | 1
`1 | ` ` 1
`2 | ` ` ` ` 2
`3 | ` ` ` ` 2 ` 4
`4 | ` ` ` ` 2 `10 ` 8
`5 | ` ` ` ` 1 `24 `32 `16

J. Awbrey, Riffs and Rotes

Cf. A007097, A050924, A061396, A062504, A062537, A062860.

Cf. A109300, A109301, A111791, A111792, A111794, A111800.

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

Jon Awbrey, Aug 28 2005

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.

			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

J. Awbrey, Riffs and Rotes

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

Jon Awbrey, Sep 01 2005 - Sep 02 2005

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.

			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 ` ? ` ? ` ? ` ? ` ? ` ? ` ? ` ?

J. Awbrey, Riffs and Rotes

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

Jon Awbrey, Aug 28 2005

nonn

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

			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` ` `
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `

J. Awbrey, Riffs and Rotes

Cf. A000079, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860.
Cf. A109300, A109301, A111791, A111792, A111793, A111794, A111800.

cp's OEIS Frontend

A111791 Positive integers sorted by rote height, as measured by A109301.

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A111793 Triangle T(g, h) = number of rotes of weight g and height h, both in gammas.

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

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

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

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