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, 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

Cf. A094870, A285491, A285492.

Sequence in context: A131393 A216476 A002326 * A064273 A257986 A327743

Adjacent sequences: A285490 A285491 A285492 * A285494 A285495 A285496

Keyword

nonn,look

Author

Peter Kagey, Apr 19 2017

Status

approved