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%I #9 Dec 05 2020 17:53:44
%S 18,60,900,360,1800,3360,14400,5040,44100,15120,508032,27720,396900,
%T 98280
%N a(n) is the smallest number k for which the width n at the diagonal is one smaller than the maximum width of the symmetric representation of sigma(k).
%C All numbers computed so far for this sequence have a symmetric representation of sigma that consists of a single region.
%C Additional values computed through 2000000 are a(16,17,18,20,21,22,24,26,28) = (110880, 793800, 221760, 332640, 1587600, 554400, 831600, 720720, 1965600).
%e a(2) = 60 = 2*2*3*5 is in the sequence since it is the smallest with width 2 at the diagonal and maximum width 3 in its symmetric representation of sigma. The widths of its 10 legs to the diagonal are: 1, 1, 2, 2, 3, 3, 3, 2, 2, 2.
%t (* Functions row[] and a237048[] are defined in A237048 *)
%t widthQ1[n_] := Module[{r=row[n], cW=0, mW=0, k}, For[k=1, k<=r, k++, cW+=(-1)^(k+1) a237048[n,k]; If[cW>mW, mW=cW]]; If[mW==cW+1 && cW>0, cW, 0]]
%t a338536[n_, b_] := Module[{list=Table[0, {b}], k, wQ}, For[k=1, k<=n, k++, wQ=widthQ1[k]; If[wQ!=0&&list[[wQ]]==0, list[[wQ]]=k]]; list]
%t Take[a338536[1000000,20],14] (* sequence data *)
%Y Cf. A235791, A237048, A237591, A237593, A249223, A338535.
%K nonn,more
%O 1,1
%A _Hartmut F. W. Hoft_, Nov 01 2020
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