

A236335


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


10



1, 1, 2, 2, 5, 4, 9, 3, 3, 6, 8, 5, 6, 9, 17, 4, 8, 15, 13, 24, 17, 13, 26, 32, 14, 7, 12, 29, 12, 18, 10, 10, 23, 35, 7, 16, 14, 30, 24, 23, 30, 46, 27, 20, 52, 15, 25, 40, 29, 40, 19, 38, 58, 18, 39, 42, 16, 69, 33, 25, 67, 43, 11, 51, 28, 11, 54, 73, 26, 27
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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



FORMULA



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=x1, 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



STATUS

approved



