OFFSET
1,3
COMMENTS
An integer can't appear more than twice in the sequence, which means the sequence tends to infinity.
An increasing version of this sequence is A236336.
LINKS
Grant Garcia, Table of n, a(n) for n = 1..10000
Dániel T. Nagy, Zoltán Lóránt Nagy, and Russ Woodroofe, The extensible No-Three-In-Line problem, arXiv:2209.01447 [math.CO], 2022.
FORMULA
a(n) = A236266(n-1) + 1. - Alois P. Heinz, Jan 23 2014
EXAMPLE
Consider a(5). The previous terms are 1,1,2,2. The value of a(5) can't be 1 because points (1,1),(2,1),(5,1) (corresponding to values a(1), a(2), a(5)) are on the same line: y=1. Points (3,2),(4,2),(5,2) are on the same line y=2, so a(5) can't be 2. Points (1,1),(3,2),(5,3) are on the same line: y=x/2+1/2, so a(5) can't be 3. Points (2,1),(3,2),(5,4) are on the same line: y=x-1, so a(5) can't be 4. Thus a(5)=5.
MATHEMATICA
b[1] = 1;
b[n_] := b[n] =
Min[Complement[Range[100],
Select[Flatten[
Table[b[k] + (n - k) (b[j] - b[k])/(j - k), {k, n - 2}, {j,
k + 1, n - 1}]], IntegerQ[#] &]]]
Table[b[k], {k, 70}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Jan 22 2014
STATUS
approved