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A157790
Least number of lattice points on two opposite sides from which every point of a square n X n lattice is visible.
2
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
1,3
COMMENTS
That is, the points are chosen from the 2n points on two opposite sides of the n X n lattice.
LINKS
Eric Weisstein's World of Mathematics, Visible Point
EXAMPLE
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).
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}]]
CROSSREFS
KEYWORD
hard,nonn
AUTHOR
T. D. Noe, Mar 06 2009
EXTENSIONS
More terms from Lars Blomberg, Nov 06 2014
STATUS
approved