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

1,2

Comments

An increasing version of A236335.

Links

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

Example

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.

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}]

Crossrefs

Cf. A229037, A185256, A236335.

Sequence in context: A241408 A039021 A295564 * A239515 A087667 A241444

Adjacent sequences: A236333 A236334 A236335 * A236337 A236338 A236339

Keyword

nonn

Author

Tanya Khovanova, Jan 22 2014

Status

approved