A030778 -id:A030778 - cp's OEIS frontend

A030777 The first list after the following procedure: starting with a list [3] and an empty list, repeatedly add the distinct values in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

3, 1, 2, 1, 3, 1, 3, 6, 2, 5, 1, 1, 7, 4, 6, 1, 3, 2, 1, 8, 5, 9, 1, 1, 2, 4, 4, 2, 10, 7, 12, 1, 1, 2, 2, 4, 5, 5, 5, 11, 10, 15, 1, 2, 1, 3, 3, 3, 5, 6, 9, 7, 12, 13, 18, 1, 2, 1, 4, 2, 4, 5, 4, 7, 8, 11, 8, 16, 15, 21, 1, 2, 1, 4, 2, 5, 4, 5, 6, 7, 9, 9, 13, 12

Offset: 1

Clark Kimberling

nonn

The length of the first row after stage k is 1, 2, 4, 7, 10, 15, 22, 31, 42, 55, 70, 87, 106, ... - Peter Kagey, Apr 09 2020

			Stage 1: [
  [3],
  []
]
Stage 2: [
  [3, 1],
     [3]
]
Stage 3: [
  [3, 1, 2, 1],
     [3, 3, 1]
]
Stage 4: [
  [3, 1, 2, 1, 3, 1, 3],
     [3, 3, 1, 3, 2, 1]
]
Stage 5: [
  [3, 1, 2, 1, 3, 1, 3, 6, 2, 5],
     [3, 3, 1, 3, 2, 1, 3, 2, 1]
]
Stage 6: [
  [3, 1, 2, 1, 3, 1, 3, 6, 2, 5, 1, 1, 7, 4, 6],
     [3, 3, 1, 3, 2, 1, 3, 2, 1, 6, 5, 3, 2, 1]
]

Peter Kagey, Table of n, a(n) for n = 1..9939 (First 80 stages)

The second row is A030778.

Cf. A030717.

def a030777_list(generations)
    rows = [[3], []]
    (2..generations).each do
        new_additions = rows.flatten.uniq.sort.reverse.map do |j|
            [rows.flatten.count(j), j]
        end
        rows = rows.zip(new_additions.transpose).map { |r, n| r + n }
    end
    rows[0]
end # Peter Kagey, Apr 09 2020

A030708 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

1, 1, 1, 3, 1, 3, 4, 1, 2, 3, 4, 6, 1, 2, 3, 4, 6, 8, 1, 2, 3, 4, 5, 6, 8, 11, 1, 2, 3, 4, 5, 6, 8, 11, 13, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 16, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 22, 1, 2

Offset: 1

Clark Kimberling

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Cf. A030707 (1st list).

Name revised in line with A030778 by Peter Munn, Oct 08 2022

A030758 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

1, 1, 3, 1, 4, 3, 1, 6, 4, 3, 2, 1, 8, 6, 4, 3, 2, 1, 11, 8, 6, 5, 4, 3, 2, 1, 13, 11, 8, 6, 5, 4, 3, 2, 1, 16, 13, 11, 10, 8, 7, 6, 5, 4, 3, 2, 1, 18, 16, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 22, 18, 16, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 25

Offset: 1

Clark Kimberling

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..1000

The first list is A030757.

Cf. A030707, A030708, A030709.

Name revised in line with A030778 by Peter Munn, Oct 08 2022

A030718 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 2, 3, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20

Offset: 1

Clark Kimberling

nonn

			Second list begins:
  1;
  1;
  1, 2;
  1, 2;
  1, 2, 3;
  1, 2, 3;
  1, 2, 3, 4;
  1, 2, 3, 4, 5;
  1, 2, 3, 4, 5, 6;
  1, 2, 3, 4, 5, 6, 7;
  1, 2, 3, 4, 5, 6, 7;
  1, 2, 3, 4, 5, 6, 7, 8;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 11;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 18;
  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 18, 20;

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A030717 (1st list).

s = t = {{1}}; Do[AppendTo[t, BinCounts[#, {1, Max[#] + 1}] &[Flatten[t]]]; AppendTo[s, Union@ Flatten@ t], {12}]; Flatten[s] (* Michael De Vlieger, Nov 15 2022, after Peter J. C. Moses at A030717 *)

Name revised in line with A030778 by Peter Munn, Oct 11 2022

A030728 The second list after the following procedure: starting with a list [3] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

3, 1, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

Offset: 1

Clark Kimberling

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..1000

The first list is A030727.

Name revised in line with A030778 by Peter Munn, Oct 08 2022

A030738 The second list after the following procedure: starting with a list [2] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

2, 1, 2, 1, 2, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 15, 16, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13

Offset: 1

Clark Kimberling

nonn

The 1st list is A030737.

Name revised in line with A030778 by Peter Munn, Oct 09 2022

A030748 The second list after the following procedure: starting with a list [4] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

4, 1, 4, 1, 2, 4, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9

Offset: 1

Clark Kimberling

nonn

The 1st list is A030747.

Name revised in line with A030778 by Peter Munn, Oct 09 2022

A030768 The second list after the following procedure: starting with a list [2] and an empty list, repeatedly add the distinct values already in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

2, 2, 1, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 15, 13, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 16, 15, 13, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 19, 18, 16, 15, 13, 12, 11, 10, 9, 8

Offset: 1

Clark Kimberling

nonn

The 1st list is A030767.

Name revised in line with A030778 by Peter Munn, Oct 09 2022

A030788 The second list after the following procedure: starting with a list [4] and an empty list, repeatedly add the distinct values already in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

Original entry on oeis.org

4, 4, 1, 4, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 14, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 17, 15, 14, 13, 12

Offset: 1

Clark Kimberling

nonn

The 1st list is A030787.

Name revised in line with A030778 by Peter Munn, Oct 09 2022

cp's OEIS Frontend

A030777 The first list after the following procedure: starting with a list [3] and an empty list, repeatedly add the distinct values in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

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A030708 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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A030758 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

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A030718 The second list after the following procedure: starting with a list [1] and an empty list, repeatedly add the distinct values already in the first list in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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A030728 The second list after the following procedure: starting with a list [3] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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A030738 The second list after the following procedure: starting with a list [2] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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A030748 The second list after the following procedure: starting with a list [4] and an empty list, repeatedly add the distinct values already in both lists in ascending order to the second list and add the corresponding frequencies of those values to the first list.

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A030768 The second list after the following procedure: starting with a list [2] and an empty list, repeatedly add the distinct values already in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

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A030788 The second list after the following procedure: starting with a list [4] and an empty list, repeatedly add the distinct values already in both lists in descending order to the second list and add the corresponding frequencies of those values to the first list.

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