A067498 Maximum number of reflections for a ray of light which reflects at n points (reflecting more than once at most or all points).

1, 3, 7, 11, 21, 27, 43, 51, 69, 83, 111, 123, 157, 171, 199, 227, 273

Offset

1,2

Comments

The maxima occur when the points of reflection are arranged at the vertices of a regular n-gon and the ray (except entering and leaving) follows the edges and diagonals of the polygon.

Links

Table of n, a(n) for n=1..17.

M. Oskar van Deventer, Point Mirror Reflection, in The Mathemagician and the Pied Puzzler edited by E. Berlekamp and T. Rodgers, A K Peters Publishers, 1999, pp. 245-251. google books.

Formula

For p prime, a(p)=p^2-p+1.

a(n) <= n^2-n+1. [Deventer eq (1)]

a(n) <= n^2-2*n+3 for even n [Deventer eq. (2)]

Crossrefs

Cf. A119959 (subsequence).

Sequence in context: A344483 A151923 A187264 * A018345 A082675 A201645

Adjacent sequences: A067495 A067496 A067497 * A067499 A067500 A067501

Keyword

more,nonn

Author

Henry Bottomley, Feb 22 2002

Status

approved