cp's OEIS Frontend

A373199 Least k such that the k-th maximal run of nonsquarefree numbers has length n. Position of first appearance of n in A053797.

%I A373199 #12 Jun 09 2024 22:15:55
%S A373199 1,2,13,68,241,6278,61921,311759,2530539
%N A373199 Least k such that the k-th maximal run of nonsquarefree numbers has length n. Position of first appearance of n in A053797.
%C A373199 A run of a sequence (in this case A013929) is an interval of positions at which consecutive terms differ by one. The a(n)-th run of nonsquarefree numbers begins with A045882 = A051681, subset of A053806.
%H A373199 Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>
%e A373199 The maximal runs of nonsquarefree numbers begin:
%e A373199    4
%e A373199    8   9
%e A373199   12
%e A373199   16
%e A373199   18
%e A373199   20
%e A373199   24  25
%e A373199   27  28
%e A373199   32
%e A373199   36
%e A373199   40
%e A373199   44  45
%e A373199   48  49  50
%e A373199   52
%e A373199   54
%e A373199   56
%e A373199   60
%e A373199   63  64
%e A373199 The a(n)-th rows are:
%e A373199      4
%e A373199      8     9
%e A373199     48    49    50
%e A373199    242   243   244   245
%e A373199    844   845   846   847   848
%e A373199 For example, (48, 49, 50) is the first maximal run of 3 nonsquarefree numbers, so a(3) = 13.
%t A373199 seq=Length/@Split[Select[Range[10000],!SquareFreeQ[#]&],#1+1==#2&];
%t A373199 spna[y_]:=Max@@Select[Range[Length[y]],SubsetQ[y,Range[#]]&];
%t A373199 Table[Position[seq,i][[1,1]],{i,spna[seq]}]
%Y A373199 For composite instead of nonsquarefree we have A073051.
%Y A373199 The version for squarefree runs is A373128.
%Y A373199 For prime instead of nonsquarefree we have A373400.
%Y A373199 A005117 lists the squarefree numbers, first differences A076259.
%Y A373199 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A373199 Cf. A007674, A020754, A045882, A120992, A061398, A061399, A068781, A101836, A251092, A294242, A373410, A373412.
%K A373199 nonn,more
%O A373199 1,2
%A A373199 _Gus Wiseman_, Jun 08 2024