A141248 Number of points having minimal visibility in a square n X n lattice of points.

1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 36, 1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 9, 4, 4, 52, 4, 4, 8, 4, 4, 44, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 12, 4, 4, 4, 4, 1, 4, 4, 4, 4, 4, 4, 4, 1, 4, 4, 4, 20, 4, 4, 4, 4, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,2

Comments

Sequence A141247 gives the minimum number of points visible from a point. By symmetry, when a(n) is odd, the central point in the lattice can see only the minimal number of points. When a(n)=1, the central point is the only such point. See A141249 for the n X n lattices that have such a central point.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Mathematica

Table[mn=n^2+1; pts=0; Do[cnt=0; Do[If[GCD[c-a, d-b]<2, cnt++ ], {a, n}, {b, n}]; If[cnt<mn, mn=cnt; pts=1, If[cnt==mn, pts++ ]], {c, n}, {d, n}]; pts, {n, 20}]

Crossrefs

Cf. A141225.

Sequence in context: A010709 A138908 A032564 * A273339 A088899 A258199

Adjacent sequences: A141245 A141246 A141247 * A141249 A141250 A141251

Keyword

nonn

Author

T. D. Noe, Jun 17 2008

Status

approved