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.

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

Cf. A229037, A248625, A285490.

Sequence in context: A323286 A193818 A127535 * A257640 A262930 A293387

Adjacent sequences: A285488 A285489 A285490 * A285492 A285493 A285494

Keyword

nonn,look

Author

Peter Kagey, Apr 19 2017

Status

approved