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A373415 Maximum of the n-th maximal run of squarefree numbers.

%I A373415 #9 Aug 02 2024 05:22:15
%S A373415 3,7,11,15,17,19,23,26,31,35,39,43,47,51,53,55,59,62,67,71,74,79,83,
%T A373415 87,89,91,95,97,103,107,111,115,119,123,127,131,134,139,143,146,149,
%U A373415 151,155,159,161,163,167,170,174,179,183,187,191,195,197,199,203,206
%N A373415 Maximum of the n-th maximal run of squarefree numbers.
%C A373415 The minimum is given by A072284.
%C A373415 A run of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by one.
%C A373415 Consists of all squarefree numbers k such that k + 1 is not squarefree.
%H A373415 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%F A373415 a(n) = A070321(A072284(n+1) - 1).
%e A373415 Row-maxima of:
%e A373415    1   2   3
%e A373415    5   6   7
%e A373415   10  11
%e A373415   13  14  15
%e A373415   17
%e A373415   19
%e A373415   21  22  23
%e A373415   26
%e A373415   29  30  31
%e A373415   33  34  35
%e A373415   37  38  39
%e A373415   41  42  43
%e A373415   46  47
%e A373415   51
%e A373415   53
%e A373415   55
%e A373415   57  58  59
%t A373415 Last/@Split[Select[Range[100],SquareFreeQ],#1+1==#2&]//Most
%Y A373415 Functional neighbors: A006093, A007674, A067774, A072284, A120992, A373413.
%Y A373415 A005117 lists the squarefree numbers, first differences A076259.
%Y A373415 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373415 Cf. A049093, A049094, A061398, A069010, A077641, A077643, A112925, A112926, A143658, A372683, A373125, A373126.
%K A373415 nonn
%O A373415 1,1
%A A373415 _Gus Wiseman_, Jun 05 2024