A157790 Least number of lattice points on two opposite sides from which every point of a square n X n lattice is visible.
1, 1, 2, 2, 3, 3, 4, 3, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 6, 4, 5, 5, 4, 4, 7, 4, 5, 5, 6, 4, 8, 4, 6, 5, 6, 4, 8, 4, 6, 5, 7, 4, 8, 4, 6, 6, 6, 4, 8, 4, 8, 5, 6, 4, 8, 5, 7, 5, 6, 4, 8, 5, 6, 6, 6, 5, 8, 4, 6, 5
Offset: 1
Examples
a(8) = 3 because all 64 points are visible from (1,1), (1,2), and (8,2). a(9) = 4 because all 81 points are visible from (1,1), (1,2), (9,1), and (9,2).
Links
- Eric Weisstein's World of Mathematics, Visible Point
Programs
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Mathematica
Join[{1}, Table[hidden=Table[{},{n^2}]; edgePts={}; Do[pt1=(c-1)*n+d; If[c==1||c==n, AppendTo[edgePts,pt1]; lst={}; Do[pt2=(a-1)*n+b; If[GCD[c-a,d-b]>1, AppendTo[lst,pt2]], {a,n}, {b,n}]; hidden[[pt1]]=lst], {c,n}, {d,n}]; edgePts=Sort[edgePts]; done=False; k=0; done=False; k=0; While[ !done, k++; len=Binomial[2n,k]; i=0; While[i
Extensions
More terms from Lars Blomberg, Nov 06 2014
Comments