A111731 Minimal size of a complete cap in (Z/nZ)^2.

4, 4, 4, 5, 4, 6, 4, 4, 4

Offset

2,1

Comments

A line in (Z/nZ)^2 is any translate of a cyclic subgroup of order n. A subset X of (Z/nZ)^2 is a cap if no three of its points are collinear and X is complete if it is not properly contained in another cap. a(n) is the minimal size of a complete cap in (Z/nZ)^2.

Links

Table of n, a(n) for n=2..10.

Jack Huizenga, The Minimum Size of Complete Caps in (Z/nZ)^2, Electron. J. Combin., 13 (2006), #R58.

Formula

If p is the smallest prime divisor of n, max{4, sqrt2p+1/2} <= a(n) <= max{4,p+1}. a(n) = 4 if n is divisible by 2 or 3.

Crossrefs

Sequence in context: A199500 A164838 A059112 * A369339 A368868 A134992

Adjacent sequences: A111728 A111729 A111730 * A111732 A111733 A111734

Keyword

nonn,more

Author

N. J. A. Sloane, Aug 01 2006

Status

approved