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A270996 T(i, j) = k is the least squarefree number with a run of exactly i>=0 nonsquarefree numbers immediately preceding k and a run of exactly j>=0 nonsquarefree numbers immediately succeeding k.

%I A270996 #26 Nov 30 2016 01:01:58
%S A270996 2,1,3,10,17,7,101,149,151,47,246,51,26,97,8474,1685,8479,727,1861,
%T A270996 241,843,22026,849,3178,2526,10826,30247,22019,217077,190453,813251,
%U A270996 55779,183553,5045,580847,826823
%N A270996 T(i, j) = k is the least squarefree number with a run of exactly i>=0 nonsquarefree numbers immediately preceding k and a run of exactly j>=0 nonsquarefree numbers immediately succeeding k.
%C A270996 The sequence a(n) = T(i, j) represents the traversal of this matrix by its successive rising antidiagonals.
%C A270996 a(2*i*(i+1)) = A270344(i), for all i >= 0.
%H A270996 Hartmut F. W. Hoft, <a href="/A270996/b270996.txt">Numbers in the first 11 antidiagonals of the matrix.</a>
%e A270996 a(13) = T(1, 3) = 97 since 96, 98, 99 and 100 are nonsquarefree while 95, 97, and 101 are squarefree, and 97 is the smallest number surrounded by the 1,3 pattern.
%e A270996 The matrix T(i, j) with first 8 complete antidiagonals together with some additional elements including the first 7 elements on the diagonal which are A270344(0)..A270344(6):
%e A270996 -------------------------------------------------------------------------
%e A270996 i\j      0       1       2       3        4         5          6        7
%e A270996 -------------------------------------------------------------------------
%e A270996 0:       2       3       7      47     8474       843      22019   826823
%e A270996 1:       1      17     151      97      241     30247     580847   217069
%e A270996 2:      10     149      26    1861    10826      5045     204322 16825126
%e A270996 3:     101      51     727    2526   183553   1944347   28591923 43811049
%e A270996 4:     246    8479    3178   55779  5876126  19375679   67806346
%e A270996 5:    1685     849  813251  450553 29002021   8061827 2082929927
%e A270996 6:   22026  190453  200854 4100277 97447622 245990821 8996188226
%e A270996 7:  217077  826831 7507930 90557979
%e A270996 T(6, 5) = 245990821, T(5, 6) = 2082929927, and all numbers in antidiagonal 11 are larger than 10^8.
%t A270996 (* The function computes the least number in the specified interval *)
%t A270996 nsfRun[n_] := Module[{i=n}, While[!SquareFreeQ[i], i++]; i-n]
%t A270996 a270996[{low_, high_},{widthL_, widthR_}] := Module[{i=low, r, s, first=0}, While[i<=high, r=nsfRun[i]; If[r != widthL, i+=r+1, s=nsfRun[i+r+1]; If[s != widthR, If[s != widthL, i+=r+s+2, i+=r+1], first=i+r; i=high+1]]]; first]
%t A270996 a270996[{0, 5000},{2, 3}] (* computes a(18) = T(2, 3) *)
%Y A270996 Cf. A005117, A007675, A068088, A073247, A073248, A073251, A228649, A268330-A268334, A270344.
%K A270996 nonn,tabl
%O A270996 0,1
%A A270996 _Hartmut F. W. Hoft_, Mar 28 2016