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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A034400 A021820 A222882 * A016724 A058657 A321285
KEYWORD
nonn
AUTHOR
Tanya Khovanova, Jan 22 2014
STATUS
approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)