A362782 a(n) is the smallest number k whose symmetric representation of sigma(k) shares sections of its border with those of n other numbers.

1, 2, 4, 6, 12, 24, 36, 60, 96, 120, 330, 360, 600, 630, 1170, 1344, 4760, 2530, 4500, 5292, 6120, 9360, 4200, 23343, 17136

Offset

1,2

Comments

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.

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.

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.

Links

Table of n, a(n) for n=1..25.

Example

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).
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).

Mathematica

(* functions path[] and a237270[] are defined in A237270 *)
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
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]
Take[a362782[25000, 30], 25] (* very long computation time *)

Crossrefs

Cf. A235791, A237270, A237271, A237591, A237593.

Sequence in context: A234517 A236021 A340637 * A365900 A365681 A333665

Adjacent sequences: A362779 A362780 A362781 * A362783 A362784 A362785

Keyword

nonn,more

Author

Hartmut F. W. Hoft, May 03 2023

Status

approved