A236336 Lexicographically earliest increasing sequence of positive integers whose graph has no three collinear points.

1, 2, 4, 5, 9, 12, 16, 22, 26, 33, 38, 45, 53, 60, 61, 76, 86, 91, 92, 97, 111, 112, 121, 134, 135, 147, 148, 150, 153, 157, 167, 180, 200, 212, 223, 227, 228, 238, 246, 264, 269, 282, 286, 305, 312, 313, 321, 322, 327, 328, 360, 374, 389, 393, 395, 420, 421

Offset: 1

Author

Tanya Khovanova, Jan 22 2014

Keywords

• nonn

Comments

An increasing version of A236335.

Examples

			Consider a(5). The previous terms are 1,2,4,5. The value of a(5) can't be 6 because points (3,4),(4,5),(5,6) (corresponding to values a(3),a(4),a(5)) are on the same line: y=x+1. Points (1,1),(3,4),(5,7) are on the same line y=3x/2-1/2, so a(5) can't be 7. Points (2,2),(3,4),(5,8) are on the same line: y=2x-2, so a(5) can't be 8. Thus a(5)=5.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A229037, A185256, A236335.

Programs

Maple

a:= proc(n) option remember; local i, j, k, ok;
      if n<3 then n
    else for k from 1+a(n-1) do ok:=true;
           for j from n-1 to 2 by -1 while ok do
             for i from j-1 to 1 by -1 while ok do
               ok:= (n-j)*(a(j)-a(i))<>(j-i)*(k-a(j)) od
           od; if ok then return k fi
         od
      fi
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, Jan 23 2014

Mathematica

g[1] = 1;
g[n_] := g[n] =
  Min[Complement[Range[g[n - 1] + 1, 500],
    Select[Flatten[
      Table[g[k] + (n - k) (g[j] - g[k])/(j - k), {k, n - 2}, {j,
        k + 1, n - 1}]], IntegerQ[#] &]]]
Table[g[k], {k, 50}]