cp's OEIS Frontend

A373128 Least k such that the k-th maximal antirun of squarefree numbers has length n. Position of first appearance of n in A373127.

%I A373128 #9 Jun 10 2024 08:52:59
%S A373128 1,3,10,8,19,162,1853,2052,1633,26661,46782,3138650,1080330
%N A373128 Least k such that the k-th maximal antirun of squarefree numbers has length n. Position of first appearance of n in A373127.
%C A373128 An antirun of a sequence (in this case A005117) is an interval of positions at which consecutive terms differ by more than one.
%H A373128 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373128 The maximal antiruns of squarefree numbers begin:
%e A373128    1
%e A373128    2
%e A373128    3   5
%e A373128    6
%e A373128    7  10
%e A373128   11  13
%e A373128   14
%e A373128   15  17  19  21
%e A373128   22
%e A373128   23  26  29
%e A373128   30
%e A373128   31  33
%e A373128   34
%e A373128   35  37
%e A373128 The a(n)-th rows are:
%e A373128     1
%e A373128     3    5
%e A373128    23   26   29
%e A373128    15   17   19   21
%e A373128    47   51   53   55   57
%e A373128   483  485  487  489  491  493
%e A373128 For example, (23, 26, 29) is the first maximal antirun of 3 squarefree numbers, so a(3) = 10.
%t A373128 t=Length/@Split[Select[Range[10000],SquareFreeQ[#]&],#1+1!=#2&]//Most;
%t A373128 spnm[y_]:=Max@@NestWhile[Most,y,Union[#]!=Range[Max@@#]&];
%t A373128 Table[Position[t,k][[1,1]],{k,spnm[t]}]
%Y A373128 For composite instead of squarefree we have A073051.
%Y A373128 Positions of first appearances in A373127.
%Y A373128 The version for nonsquarefree runs is A373199, firsts of A053797.
%Y A373128 For prime instead of squarefree we have A373401, firsts of A027833.
%Y A373128 A005117 lists the squarefree numbers, first differences A076259.
%Y A373128 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373128 Cf. A006512, A007674, A049093, A068781, A072284, A077641, A120992, A174965, A251092, A373198, A373408, A373411.
%K A373128 nonn,more
%O A373128 1,2
%A A373128 _Gus Wiseman_, Jun 08 2024