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A333253
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Lengths of maximal strictly increasing subsequences in the sequence of prime gaps (A001223).
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12
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2, 2, 2, 3, 2, 1, 3, 1, 2, 1, 2, 3, 1, 2, 3, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 1, 3, 3, 2, 2, 3, 1, 3, 1, 2, 3, 2, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 1, 3, 1, 2, 4, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 1, 3, 1, 3, 3, 1, 2, 2, 2
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OFFSET
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1,1
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COMMENTS
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Prime gaps are differences between adjacent prime numbers.
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LINKS
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FORMULA
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Partial sums are A333231. The partial sum up to but not including the n-th one is A333382(n).
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EXAMPLE
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The prime gaps split into the following strictly increasing subsequences: (1,2), (2,4), (2,4), (2,4,6), (2,6), (4), (2,4,6), (6), (2,6), (4), (2,6), (4,6,8), (4), (2,4), (2,4,14), ...
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MATHEMATICA
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Length/@Split[Differences[Array[Prime, 100]], #1<#2&]//Most
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CROSSREFS
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The weakly decreasing version is A333212.
The weakly increasing version is A333215.
First differences of A333231 (if its first term is 0).
The strictly decreasing version is A333252.
Strictly increasing runs of compositions in standard order are A124768.
Positions of strict ascents in the sequence of prime gaps are A258025.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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