A373128 - OEIS

%I #9 Jun 10 2024 08:52:59

%S 1,3,10,8,19,162,1853,2052,1633,26661,46782,3138650,1080330

%N Least k such that the k-th maximal antirun of squarefree numbers has length n. Position of first appearance of n in A373127.

%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    23   26   29

%e    15   17   19   21

%e    47   51   53   55   57

%e   483  485  487  489  491  493

%e For example, (23, 26, 29) is the first maximal antirun of 3 squarefree numbers, so a(3) = 10.

%t t=Length/@Split[Select[Range[10000],SquareFreeQ[#]&],#1+1!=#2&]//Most;

%t spnm[y_]:=Max@@NestWhile[Most,y,Union[#]!=Range[Max@@#]&];

%t Table[Position[t,k][[1,1]],{k,spnm[t]}]

%Y For composite instead of squarefree we have A073051.

%Y Positions of first appearances in A373127.

%Y The version for nonsquarefree runs is A373199, firsts of A053797.

%Y For prime instead of squarefree we have A373401, firsts of A027833.

%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, A120992, A174965, A251092, A373198, A373408, A373411.

%K nonn,more

%O 1,2

%A _Gus Wiseman_, Jun 08 2024