

A236335


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


9



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.
a(n)  1 = A236266(n1).  Alois P. Heinz, Jan 23 2014


LINKS

Grant Garcia, Table of n, a(n) for n = 1..10000


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

Cf. A229037, A185256, A231334, A236266, A236336, A300002.
Sequence in context: A034400 A021820 A222882 * A016724 A058657 A321285
Adjacent sequences: A236332 A236333 A236334 * A236336 A236337 A236338


KEYWORD

nonn


AUTHOR

Tanya Khovanova, Jan 22 2014


STATUS

approved



