%I #10 Jun 11 2024 00:20:53
%S 1,3,8,10,19,162,1633,1853,2052,26661,46782,1080330,3138650
%N 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 The unsorted version is A373128.
%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 The maximal antiruns of squarefree numbers begin:
%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 The a(n)-th rows are:
%e 1
%e 3 5
%e 15 17 19 21
%e 23 26 29
%e 47 51 53 55 57
%e 483 485 487 489 491 493
%t t=Length/@Split[Select[Range[10000],SquareFreeQ],#1+1!=#2&]//Most;
%t Select[Range[Length[t]],FreeQ[Take[t,#-1],t[[#]]]&]
%Y For squarefree runs we have the triple (1,3,5), firsts of A120992.
%Y For prime runs we have the triple (1,2,3), firsts of A175632.
%Y The unsorted version is A373128, firsts of A373127.
%Y For nonsquarefree runs we have A373199 (assuming sorted), firsts of A053797.
%Y For composite runs we have A373400, unsorted A073051.
%Y For prime antiruns we have A373402, unsorted A373401, firsts of A027833.
%Y For composite antiruns we have the triple (1,2,7), firsts of A373403.
%Y A005117 lists the squarefree numbers, first differences A076259.
%Y A013929 lists the nonsquarefree numbers, first differences A078147.
%Y Cf. A006512, A007674, A049093, A068781, A072284, A077641, A174965, A251092, A373198, A373408, A373411.
%K nonn,more
%O 1,2
%A _Gus Wiseman_, Jun 10 2024