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A373127 Length of the n-th maximal antirun of squarefree numbers differing by more than one.

%I A373127 #6 Jun 07 2024 08:03:17
%S A373127 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 A373127 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 A373127 2,2,1,2,1,2,1,2,1,2,2,1,4,1,3,4,1,2,1
%N A373127 Length of the n-th maximal antirun of squarefree numbers differing by more than one.
%C A373127 The sum of this antirun is given by A373411.
%C A373127 An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.
%H A373127 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373127 Row-lengths of:
%e A373127    1
%e A373127    2
%e A373127    3  5
%e A373127    6
%e A373127    7 10
%e A373127   11 13
%e A373127   14
%e A373127   15 17 19 21
%e A373127   22
%e A373127   23 26 29
%e A373127   30
%e A373127   31 33
%e A373127   34
%e A373127   35 37
%e A373127   38
%e A373127   39 41
%e A373127   42
%e A373127   43 46
%e A373127   47 51 53 55 57
%t A373127 Length/@Split[Select[Range[100],SquareFreeQ],#1+1!=#2&]
%Y A373127 Positions of first appearances are A373128, sorted A373200.
%Y A373127 Functional neighbors: A007674, A027833 (partial sums A029707), A120992, A373403, A373408, A373409, A373411.
%Y A373127 A005117 lists the squarefree numbers, first differences A076259.
%Y A373127 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373127 A077643 counts squarefree numbers with n bits, sum A373123.
%Y A373127 Cf. A049093, A049094, A061398, A077641, A112925, A112926, A174965, A350842, A372683, A373125, A373126, A373197, A373198.
%K A373127 nonn
%O A373127 1,3
%A A373127 _Gus Wiseman_, Jun 05 2024