A285490 -id:A285490 - cp's OEIS frontend

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

Peter Kagey, Apr 19 2017

No three terms a(j), a(j+k), a(j+2k) (for any j and k) form an arithmetic progression.

			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.

Giovanni Resta, Table of n, a(n) for n = 1..4000 (first 650 terms from Peter Kagey)

Cf. A229037, A248625, A285490.

A285492 a(n) is the least positive integer not already appearing such that no two distinct, unordered pairs of distinct points ((n, a(n)), (m, a(m))) and ((k, a(k)), (j, a(j))) have the same midpoint.

Original entry on oeis.org

1, 2, 3, 5, 4, 8, 11, 6, 15, 12, 9, 7, 20, 25, 16, 30, 36, 10, 18, 47, 27, 38, 59, 13, 58, 73, 43, 81, 19, 26, 96, 14, 45, 109, 121, 72, 54, 44, 70, 17, 98, 137, 60, 156, 29, 113, 155, 92, 22, 145, 173, 63, 112, 46, 39, 136, 204, 24, 219, 174, 21, 237, 253, 80

Offset: 1

Peter Kagey, Apr 19 2017

			a(4) != 4 or else midpoint((4,4), (1,1)) = midpoint((2,2), (3,3)), thus
a(4) = 5.
a(6) != 6 or else midpoint((6,6), (3,3)) = midpoint((4,5), (5,4));
a(6) != 7 or else midpoint((6,7), (1,1)) = midpoint((3,3), (4,5)); thus
a(6) = 8.

Giovanni Resta, Table of n, a(n) for n = 1..3000 (first 650 terms from Peter Kagey)

Cf. A285490.

cp's OEIS Frontend

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.

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