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%I #12 Jun 11 2023 11:39:10
%S 1,2,4,6,12,24,36,60,96,120,330,360,600,630,1170,1344,4760,2530,4500,
%T 5292,6120,9360,4200,23343,17136
%N a(n) is the smallest number k whose symmetric representation of sigma(k) shares sections of its border with those of n other numbers.
%C The values of the first 6 numbers in this sequence can be read off from the illustration of the symmetric representations of sigma, SRS, in A237593.
%C SRS(a(5)) = SRS(12) consists of 1 part. It has SRS(10) and SRS(15) as its farthest ones with shared border sections, neither one consists of a single part.
%C SRS(a(18)) = SRS(2530) consists of 2 parts while its farthest shared border sections are with SRS(2520) and SRS(2538) both of which consist of a single part.
%e a(4) = 6 since the borders of SRS(4) and SRS(5) below and SRS(7) and SRS(8) above share border sections with SRS(6).
%e a(5) = 12 since the borders of SRS(10) and SRS(11) below and SRS(13), SRS(14) and SRS(15) above share border sections with SRS(12). SRS(9) is not included since it only shares one vertex (on the diagonal) with SRS(12).
%t (* functions path[] and a237270[] are defined in A237270 *)
%t touchQ[{i_, j_}] := Module[{upi=Transpose[{Most[path[i]], Rest[path[i]]}], loj=Transpose[{Most[path[j-1]], Rest[path[j-1]]}]}, Intersection[upi, loj]!={}]/;i<j
%t a362782[n_, b_] := Module[{list=Join[{1}, Table[0, b-1]], k=2, i, j, r}, While[k<=n, i=k-1; While[touchQ[{i, k}], i--]; j=k+1; While[touchQ[{k, j}], j++]; r=j-i-2; If[list[[r]]==0, list[[r]]=k]; If[Length[a237270[j]]==1, k=j, k++]]; list]
%t Take[a362782[25000,30], 25] (* very long computation time *)
%Y Cf. A235791, A237270, A237271, A237591, A237593.
%K nonn,more
%O 1,2
%A _Hartmut F. W. Hoft_, May 03 2023
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