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A333253 Lengths of maximal strictly increasing subsequences in the sequence of prime gaps (A001223). 12
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Prime gaps are differences between adjacent prime numbers.
LINKS
FORMULA
Partial sums are A333231. The partial sum up to but not including the n-th one is A333382(n).
EXAMPLE
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), ...
MATHEMATICA
Length/@Split[Differences[Array[Prime, 100]], #1<#2&]//Most
CROSSREFS
The weakly decreasing version is A333212.
The weakly increasing version is A333215.
The unequal version is A333216.
First differences of A333231 (if its first term is 0).
The strictly decreasing version is A333252.
The equal version is A333254.
Prime gaps are A001223.
Strictly increasing runs of compositions in standard order are A124768.
Positions of strict ascents in the sequence of prime gaps are A258025.
Sequence in context: A273021 A365722 A071137 * A193990 A089367 A130192
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 18 2020
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)