

A333212


Lengths of maximal weakly decreasing subsequences in the sequence of prime gaps (A001223).


12



1, 2, 2, 2, 1, 2, 3, 1, 3, 3, 2, 1, 3, 2, 1, 2, 2, 2, 3, 3, 2, 2, 4, 1, 2, 5, 3, 1, 3, 1, 2, 2, 1, 1, 4, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 1, 2, 2, 4, 1, 4, 4, 3, 1, 3, 2, 1, 1, 2, 5, 3, 2, 2, 2, 2, 2, 1, 3, 1, 3, 1, 2, 1, 3, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 3
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OFFSET

1,2


COMMENTS

Prime gaps are differences between adjacent prime numbers.


LINKS



FORMULA

Ones correspond to weak prime quartets A054819, so the sum of terms up to but not including the nth one is A000720(A054819(n  1)).


EXAMPLE

The prime gaps split into the following weakly decreasing subsequences: (1), (2,2), (4,2), (4,2), (4), (6,2), (6,4,2), (4), (6,6,2), (6,4,2), (6,4), (6), ...


MATHEMATICA

Length/@Split[Differences[Array[Prime, 100]], #1>=#2&]//Most


CROSSREFS

First differences of A258025 (with zero prepended).
The version for the Kolakoski sequence is A332273.
The weakly increasing version is A333215.
The strictly decreasing version is A333252.
The strictly increasing version is A333253.
Positions of adjacent equal differences are A064113.
Weakly decreasing runs of compositions in standard order are A124765.
Positions of strict ascents in the sequence of prime gaps are A258025.
Cf. A000040, A000720, A001221, A036263, A054819, A084758, A114994, A124760, A124761, A124768, A333213, A333214.


KEYWORD

nonn


AUTHOR



STATUS

approved



