A141248 -id:A141248 - cp's OEIS frontend

A141247 Minimum number of points visible from a point in a square n X n lattice.

1, 4, 6, 10, 14, 22, 26, 38, 46, 58, 66, 86, 94, 118, 130, 146, 162, 194, 206, 241, 257, 282, 302, 346, 362, 401, 426, 462, 486, 542, 558, 609, 641, 690, 722, 770, 794, 861, 899, 950, 982, 1062, 1086, 1157, 1201, 1258, 1302, 1393, 1425, 1501, 1546, 1613

Offset: 1

T. D. Noe, Jun 17 2008

nonn

Two points (a,b) and (c,d) are visible to each other when gcd(c-a,d-b)=1. Sequence A141248 gives the number of lattice points that have minimal visibility.

T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein, MathWorld: Visible Point

Cf. A141224.

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

The minimum number of visible points is slightly less than c*n^2, with c = 6/pi^2.

A141249 Numbers n such that the central point of the square n X n lattice sees the minimal number of points.

Original entry on oeis.org

1, 21, 33, 45, 73, 81, 193, 201, 241, 273, 313, 381, 421, 445, 453, 661, 693, 861, 885, 913

Offset: 1

T. D. Noe, Jun 17 2008

nonn

These n are the numbers for which A141248(n) is odd. Note that n must be odd. When A141248(n)=1, the central point is the only point seeing the minimal number of points. These numbers are 1 or 9 (mod 12). These numbers also seem to produce cubic n X n X n lattices in which the central point has minimal visibility. Note that for n>1, n+1 is twice a prime power in A141250.

Cf. A141226.

cp's OEIS Frontend

A141247 Minimum number of points visible from a point in a square n X n lattice.

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