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Length of the n-th maximal antirun of squarefree numbers differing by more than one.
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%I #6 Jun 07 2024 08:03:17

%S 1,1,2,1,2,2,1,4,1,3,1,2,1,2,1,2,1,2,5,1,2,2,1,2,1,2,2,1,2,2,1,4,1,3,

%T 1,2,1,2,1,2,1,2,2,3,1,2,2,1,2,1,2,4,2,1,4,1,3,2,1,2,1,2,1,2,2,1,4,1,

%U 2,2,1,2,1,2,1,2,1,2,2,1,4,1,3,4,1,2,1

%N Length of the n-th maximal antirun of squarefree numbers differing by more than one.

%C The sum of this antirun is given by A373411.

%C An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.

%H Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>

%e Row-lengths of:

%e 1

%e 2

%e 3 5

%e 6

%e 7 10

%e 11 13

%e 14

%e 15 17 19 21

%e 22

%e 23 26 29

%e 30

%e 31 33

%e 34

%e 35 37

%e 38

%e 39 41

%e 42

%e 43 46

%e 47 51 53 55 57

%t Length/@Split[Select[Range[100],SquareFreeQ],#1+1!=#2&]

%Y Positions of first appearances are A373128, sorted A373200.

%Y Functional neighbors: A007674, A027833 (partial sums A029707), A120992, A373403, A373408, A373409, A373411.

%Y A005117 lists the squarefree numbers, first differences A076259.

%Y A013929 lists the nonsquarefree numbers, first differences A078147.

%Y A077643 counts squarefree numbers with n bits, sum A373123.

%Y Cf. A049093, A049094, A061398, A077641, A112925, A112926, A174965, A350842, A372683, A373125, A373126, A373197, A373198.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jun 05 2024