3,1

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Borwein and Moser, A survey of Sylvester's problem and its generalizations, Aequat. Math., 40 (1990), 111-135.

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.

Kelly and Moser showed that a(n) >= ceiling(3n/7); Hansen showed that a(n) >= floor(n/2) except for n=7 and 13.

Sequence in context: A005536 A080038 A121937 this_sequence A091282 A046537 A167596

Adjacent sequences: A003031 A003032 A003033 this_sequence A003035 A003036 A003037

nonn,hard,nice

N. J. A. Sloane (njas(AT)research.att.com).