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Search: id:A157791
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| A157791 |
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Least number of lattice points on two adjacent sides from which every point of a square n x n lattice is visible. |
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+0
3
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| 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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That is, the points are chosen from the 2n-1 points on two adjacent sides of the n x n lattice.
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LINKS
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Eric Weisstein, MathWorld: Visible Point
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EXAMPLE
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a(11)= 4 because all 121 points are visible from (1,1), (1,2), (2,1), or (1,4).
a(25)= 4 because all 625 points are visible from (1,2), (4,1), (6,1), or (23,1).
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MATHEMATICA
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Join[{1}, Table[hidden=Table[{}, {n^2}]; edgePts={}; Do[pt1=(c-1)*n+d; If[c==1||d==1, 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-1, 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
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A157639, A157720, A157790, A157792
Sequence in context: A084556 A084506 A071578 this_sequence A156874 A078767 A093125
Adjacent sequences: A157788 A157789 A157790 this_sequence A157792 A157793 A157794
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KEYWORD
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hard,more,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 06 2009
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