A157791 Least number of lattice points on two adjacent sides from which every point of a square n X n lattice is visible.

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, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset

1,3

Comments

That is, the points are chosen from the 2n-1 points on two adjacent sides of the n X n lattice.

Links

Table of n, a(n) for n=1..87.

Eric Weisstein's World of Mathematics, Visible Point

Example

a(11)= 4 because all 121 points are visible from (1,1), (1,2), (2,1), and (1,4).
a(25)= 4 because all 625 points are visible from (1,2), (4,1), (6,1), and (23,1).

Mathematica

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}]]

Crossrefs

Cf. A157639, A157720, A157790, A157792.

Sequence in context: A084506 A071578 A364800 * A236857 A156874 A294234

Adjacent sequences: A157788 A157789 A157790 * A157792 A157793 A157794

Keyword

hard,nonn

Author

T. D. Noe, Mar 06 2009

Extensions

More terms from Lars Blomberg, Nov 06 2014

Status

approved