A030757
The first 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, 1, 2, 6, 1, 2, 3, 1, 8, 1, 2, 3, 5, 3, 11, 1, 2, 3, 1, 4, 8, 5, 13, 1, 2, 4, 4, 3, 6, 10, 7, 16, 1, 2, 3, 1, 5, 1, 6, 4, 9, 12, 9, 18, 1, 2, 3, 1, 4, 2, 2, 6, 2, 8, 6, 11, 14, 11, 22, 1, 2, 3, 1, 4, 2, 7, 3, 3, 8, 3, 11, 7, 13, 16, 16, 25, 1, 2, 3
Offset: 1
A030727
The first 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, 1, 2, 3, 1, 3, 5, 2, 6, 6, 4, 7, 1, 1, 9, 5, 8, 1, 2, 3, 1, 12, 7, 10, 2, 4, 4, 2, 1, 1, 15, 10, 11, 5, 5, 5, 4, 2, 2, 1, 1, 18, 13, 12, 7, 9, 6, 5, 3, 3, 3, 1, 2, 1, 21, 15, 16, 8, 11, 8, 7, 4, 5, 4, 2, 4, 1, 2, 1, 24, 18, 17, 12, 13, 9, 9, 7, 6, 5, 4, 5
Offset: 1
A030778
The second 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.
Original entry on oeis.org
3, 3, 1, 3, 2, 1, 3, 2, 1, 6, 5, 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, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 15, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 21, 18, 16, 15, 13, 12, 11, 10, 9, 8, 7
Offset: 1
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]
]
-
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[1]
end # Peter Kagey, Apr 09 2020
A030737
The first 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, 1, 2, 3, 4, 4, 5, 1, 1, 7, 6, 2, 3, 1, 9, 8, 4, 4, 2, 1, 1, 12, 10, 5, 7, 3, 2, 2, 1, 1, 15, 13, 7, 8, 5, 3, 4, 2, 2, 1, 1, 18, 16, 9, 10, 7, 4, 6, 4, 3, 2, 2, 1, 1, 21, 19, 11, 13, 8, 6, 8, 5, 5, 4, 3, 2, 2, 1, 1, 24, 22, 13, 15, 11, 8, 9, 8, 6, 5, 1, 4
Offset: 1
A030747
The first 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, 1, 2, 3, 1, 3, 5, 2, 2, 4, 6, 5, 3, 6, 1, 8, 6, 5, 7, 3, 2, 9, 8, 7, 8, 5, 4, 1, 1, 12, 9, 8, 10, 7, 5, 3, 4, 1, 14, 10, 10, 12, 9, 6, 5, 6, 3, 1, 1, 17, 11, 12, 13, 11, 9, 6, 7, 5, 4, 3, 1, 19, 12, 14, 15, 13, 11, 8, 8, 7, 5, 2, 5, 1, 2, 1, 22, 15, 15, 16
Offset: 1
A030767
The first 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, 1, 2, 1, 4, 3, 1, 1, 5, 4, 1, 3, 2, 6, 7, 1, 1, 2, 4, 4, 8, 9, 1, 1, 2, 2, 3, 7, 5, 10, 12, 1, 1, 2, 2, 4, 3, 5, 8, 7, 13, 15, 1, 1, 2, 2, 3, 4, 6, 4, 7, 10, 9, 16, 18, 1, 1, 2, 2, 3, 4, 5, 5, 8, 6, 8, 13, 11, 19, 21, 1, 1, 2, 2, 3, 4, 4, 1, 5, 6, 8, 9, 8, 11, 15
Offset: 1
A030787
The first 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, 1, 2, 1, 3, 1, 3, 4, 2, 2, 5, 1, 6, 3, 5, 6, 2, 3, 7, 5, 6, 8, 1, 1, 4, 5, 8, 7, 8, 9, 1, 4, 3, 5, 7, 10, 8, 9, 12, 1, 1, 3, 6, 5, 6, 9, 12, 10, 10, 14, 1, 3, 4, 5, 7, 6, 9, 11, 13, 12, 11, 17, 1, 2, 1, 5, 2, 5, 7, 8, 8, 11, 13, 15, 14, 12, 19, 1, 2, 1, 4, 3
Offset: 1
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