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A157790
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Least number of lattice points on two opposite sides from which every point of a square n x n lattice is visible.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| That is, the points are chosen from the 2n points on two opposite sides of the n x n lattice.
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LINKS
| Eric Weisstein, MathWorld: Visible Point
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EXAMPLE
| a(8) = 3 because all 64 points are visible from (1,1), (1,2), or (8,2).
a(9) = 4 because all 81 points are visible from (1,1), (1,2), (9,1), or (9,2).
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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<len, i++; s=Subsets[edgePts, {k}, {i}][[1]]; If[Intersection@@hidden[[s]]=={}, done=True; Break[]]]]; k, {n, 2, 11}]]
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CROSSREFS
| A157639, A157720, A157791, A157792
Sequence in context: A057935 A124831 A105096 * A070241 A066412 A196048
Adjacent sequences: A157787 A157788 A157789 * A157791 A157792 A157793
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KEYWORD
| hard,more,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Mar 06 2009
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