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 A111731 Minimal size of a complete cap in (Z/nZ)^2. 0
 4, 4, 4, 5, 4, 6, 4, 4, 4 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 14 13:32 EDT 2024. Contains 375165 sequences. (Running on oeis4.)