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URL: https://oeis.org/A285493

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A285493
a(n) is the least positive integer not already appearing 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.
1
1, 2, 4, 3, 6, 10, 15, 5, 13, 9, 18, 29, 7, 25, 37, 8, 22, 14, 41, 48, 23, 58, 11, 66, 32, 78, 24, 52, 83, 12, 73, 93, 26, 60, 42, 118, 21, 89, 65, 106, 139, 145, 19, 84, 16, 162, 76, 43, 173, 183, 199, 123, 87, 30, 28, 161, 101, 56, 116, 55, 235, 182, 150
OFFSET
1,2
COMMENTS
No three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression.
Conjecture: This is a permutation of the positive integers.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..3000 (first 650 terms from Peter Kagey)
EXAMPLE
a(3) != 3 or else midpoint((3,3), (1,1)) = midpoint((2,2), (2,2)), thus
a(3) = 4.
a(6) != 5 or else midpoint((6,5), (3,4)) = midpoint((4,3), (5,6));
a(6) != 7 or else midpoint((6,7), (1,1)) = midpoint((2,2), (5,6));
a(6) != 8 or else midpoint((6,8), (2,2)) = midpoint((3,4), (5,6));
a(6) != 9 or else midpoint((6,9), (4,3)) = midpoint((5,6), (5,6)); thus
a(6) = 10.
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Peter Kagey, Apr 19 2017
STATUS
approved