cp's OEIS Frontend

A373573 Least k such that the k-th maximal antirun of nonsquarefree numbers has length n. Position of first appearance of n in A373409.

%I A373573 #6 Jun 11 2024 09:36:44
%S A373573 6,1,18,8,4,2,10,52,678
%N A373573 Least k such that the k-th maximal antirun of nonsquarefree numbers has length n. Position of first appearance of n in A373409.
%C A373573 The sorted version is A373574.
%C A373573 An antirun of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by more than one.
%C A373573 Is this sequence finite? Are there only 9 terms?
%H A373573 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373573 The maximal antiruns of nonsquarefree numbers begin:
%e A373573    4   8
%e A373573    9  12  16  18  20  24
%e A373573   25  27
%e A373573   28  32  36  40  44
%e A373573   45  48
%e A373573   49
%e A373573   50  52  54  56  60  63
%e A373573   64  68  72  75
%e A373573   76  80
%e A373573   81  84  88  90  92  96  98
%e A373573   99
%e A373573 The a(n)-th rows are:
%e A373573     49
%e A373573      4    8
%e A373573    148  150  152
%e A373573     64   68   72   75
%e A373573     28   32   36   40   44
%e A373573      9   12   16   18   20   24
%e A373573     81   84   88   90   92   96   98
%e A373573    477  480  484  486  488  490  492  495
%e A373573   6345 6348 6350 6352 6354 6356 6358 6360 6363
%t A373573 t=Length/@Split[Select[Range[10000],!SquareFreeQ[#]&],#1+1!=#2&]//Most;
%t A373573 spna[y_]:=Max@@Select[Range[Length[y]],SubsetQ[t,Range[#1]]&];
%t A373573 Table[Position[t,k][[1,1]],{k,spna[t]}]
%Y A373573 For composite runs we have A073051, firsts of A176246, sorted A373400.
%Y A373573 For squarefree runs we have the triple (5,3,1), firsts of A120992.
%Y A373573 For prime runs we have the triple (1,3,2), firsts of A175632.
%Y A373573 For squarefree antiruns we have A373128, firsts of A373127, sorted A373200.
%Y A373573 For nonsquarefree runs we have A373199 (assuming sorted), firsts of A053797.
%Y A373573 For prime antiruns we have A373401, firsts of A027833, sorted A373402.
%Y A373573 For composite antiruns we have the triple (2,7,1), firsts of A373403.
%Y A373573 Positions of first appearances in A373409.
%Y A373573 The sorted version is A373574.
%Y A373573 A005117 lists the squarefree numbers, first differences A076259.
%Y A373573 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373573 Cf. A007674, A025157, A049094, A061399, A068781, A072284, A110969, A251092, A294242, A373410, A373412.
%K A373573 nonn
%O A373573 1,1
%A A373573 _Gus Wiseman_, Jun 10 2024