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A373200 Numbers k such that the k-th maximal antirun of squarefree numbers has length different from all prior maximal antiruns. Sorted positions of first appearances in A373127.

%I A373200 #10 Jun 11 2024 00:20:53
%S A373200 1,3,8,10,19,162,1633,1853,2052,26661,46782,1080330,3138650
%N A373200 Numbers k such that the k-th maximal antirun of squarefree numbers has length different from all prior maximal antiruns. Sorted positions of first appearances in A373127.
%C A373200 The unsorted version is A373128.
%C A373200 An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.
%H A373200 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.
%e A373200 The maximal antiruns of squarefree numbers begin:
%e A373200    1
%e A373200    2
%e A373200    3   5
%e A373200    6
%e A373200    7  10
%e A373200   11  13
%e A373200   14
%e A373200   15  17  19  21
%e A373200   22
%e A373200   23  26  29
%e A373200   30
%e A373200   31  33
%e A373200   34
%e A373200   35  37
%e A373200 The a(n)-th rows are:
%e A373200     1
%e A373200     3    5
%e A373200    15   17   19   21
%e A373200    23   26   29
%e A373200    47   51   53   55   57
%e A373200   483  485  487  489  491  493
%t A373200 t=Length/@Split[Select[Range[10000],SquareFreeQ],#1+1!=#2&]//Most;
%t A373200 Select[Range[Length[t]],FreeQ[Take[t,#-1],t[[#]]]&]
%Y A373200 For squarefree runs we have the triple (1,3,5), firsts of A120992.
%Y A373200 For prime runs we have the triple (1,2,3), firsts of A175632.
%Y A373200 The unsorted version is A373128, firsts of A373127.
%Y A373200 For nonsquarefree runs we have A373199 (assuming sorted), firsts of A053797.
%Y A373200 For composite runs we have A373400, unsorted A073051.
%Y A373200 For prime antiruns we have A373402, unsorted A373401, firsts of A027833.
%Y A373200 For composite antiruns we have the triple (1,2,7), firsts of A373403.
%Y A373200 A005117 lists the squarefree numbers, first differences A076259.
%Y A373200 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373200 Cf. A006512, A007674, A049093, A068781, A072284, A077641, A174965, A251092, A373198, A373408, A373411.
%K A373200 nonn,more
%O A373200 1,2
%A A373200 _Gus Wiseman_, Jun 10 2024