cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A141225 Number of points having maximal visibility in a square n x n lattice.

Original entry on oeis.org

1, 4, 1, 4, 8, 16, 8, 12, 16, 36, 9, 60, 16, 16, 8, 12, 12, 12, 12, 36, 16, 16, 25, 4, 16, 8, 5, 12, 24, 64, 12, 8, 4, 4, 25, 16, 4, 8, 1, 20, 16, 4, 20, 12, 4, 4, 9, 8, 4, 4, 4, 4, 12, 4, 4, 4, 4, 12, 9, 4, 8, 4, 8, 12, 8, 4, 4, 8, 4, 16, 12, 20, 4, 8, 4, 4, 16, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 4
Offset: 1

Views

Author

T. D. Noe, Jun 15 2008

Keywords

Comments

Sequence A141224 gives the maximum number of points visible from some point. By symmetry, when a(n) is odd, the central point in the lattice can see the maximal number of points. When a(n)=1, the central point is the only such point. See A141226 for the n x n lattices that have such a central point.

Links

Programs

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

A141228 Number of points having maximal visibility in a cubic n x n x n lattice.

Original entry on oeis.org

1, 8, 1, 8, 20, 64, 20, 32, 64, 216, 13, 432, 64, 64, 20, 32, 8, 32, 32, 216, 64, 64, 27, 8, 64, 216, 7, 32, 64, 352, 32, 216, 8, 8, 125, 64, 8, 24, 1, 8, 64, 8, 32, 24, 8, 8, 27, 8, 8, 8
Offset: 1

Views

Author

T. D. Noe, Jun 15 2008

Keywords

Comments

Sequence A141227 gives the maximum number of points visible from some point. By symmetry, when a(n) is odd, the central point in the lattice can see the maximal number of points. When a(n)=1, the central point is the only such point. Apparently the numbers n in A141226 produce both the n x n and n x n x n lattices having central points with maximum visibility.

Crossrefs

Cf. A141225.

Programs

  • Mathematica
    Table[mx=0; pts=0; Do[cnt=0; Do[If[GCD[d-a,e-b,f-c]<2, cnt++ ], {a,n}, {b,n}, {c,n}]; If[cnt>mx, mx=cnt; pts=1, If[cnt==mx, pts++ ]], {d,n}, {e,n}, {f,n}]; pts, {n,10}]

A141246 Prime numbers related to maximal visibility in the square n X n lattice.

Original entry on oeis.org

5, 11, 13, 17, 19, 23, 29, 47, 73, 83, 89, 103, 109, 113, 139, 173, 181, 199, 271, 283, 293, 313, 383, 389, 467
Offset: 1

Views

Author

T. D. Noe, Jun 17 2008

Keywords

Comments

The numbers in A141226 greater than 3 are 2*a(n)+1.

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

Views

Author

T. D. Noe, Jun 17 2008

Keywords

Comments

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.

Crossrefs

Cf. A141226.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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