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COMMENTS
| An ordinary line contains exactly 2 points. The problem is to place n points, not all on a line, so as to minimize the number of ordinary lines.
Pach and Sharir give the following table for n >= 3: 3, 3, 4, 3, 3, 4, 6, 5, 6, 6, 6, 7, ?, 8, ?, 9, ?, ?, ?, 22, ... - N. J. A. Sloane, Dec 01 2010
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REFERENCES
| Borwein and Moser, A survey of Sylvester's problem and its generalizations, Aequat. Math., 40 (1990), 111-135.
J. Brakke, Some new values for Sylvester's function for n collinear points, J. Undergrad. Math., 4 (1972), 11-14.
H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, F12.
D. W. Crowe and T. A. McKee, Sylvester's problem on collinear points, Math. Mag., 41 (1968), 30-34.
B. Gr\"{u}nbaum, Arrangements and Spreads. American Mathematical Society, Providence, RI, 1972, p. 18.
S. Hansen, Contributions to the Sylvester-Gallai theory, Dissertation, Univ. Copenhagen, 1981.
L. M. Kelley and W. O. J. Moser, On the number of ordinary lines determined by n points, Canad. J. Math., 10 (1958), 210-219.
J. Pach and M. Sharir, Combinatorial Geometry and Its Algorithmic Applications, Amer. Math. Soc., 2009; see p. 2.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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