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URL: https://oeis.org/A285491

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A285491
Lexicographically earliest sequence of positive integers such that no two distinct unordered pairs of points ((n, a(n)), (m, a(m))) and ((k, a(k)), (j, a(j))) have the same midpoint.
4
1, 1, 2, 1, 4, 6, 2, 9, 1, 13, 8, 19, 2, 15, 12, 28, 32, 6, 4, 18, 43, 1, 51, 16, 36, 41, 28, 34, 2, 57, 66, 10, 80, 5, 31, 24, 61, 71, 89, 12, 107, 128, 18, 99, 42, 1, 123, 142, 10, 38, 78, 164, 120, 21, 1, 58, 183, 169, 99, 93, 203, 22, 200, 155, 7, 130, 228
OFFSET
1,3
COMMENTS
No three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..4000 (first 650 terms from Peter Kagey)
EXAMPLE
For n = 3:
a(3) != 1 or else midpoint((1, 1), (3, 1)) = midpoint((2, 1), (2, 1)), so
a(3) = 2.
For n = 5:
a(5) != 1 or else midpoint((1, 1), (5, 1)) = midpoint((2, 1), (4, 1));
a(5) != 2 or else midpoint((2, 1), (5, 2)) = midpoint((3, 2), (4, 1));
a(5) != 3 or else midpoint((1, 1), (5, 3)) = midpoint((3, 2), (3, 2)); so
a(5) = 4.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Peter Kagey, Apr 19 2017
STATUS
approved