A380968 Lexicographically earliest sequence of positive integers such that for any value k, no two sets of one or more indices at which k occurs have the same mean.

1, 1, 2, 1, 2, 2, 3, 1, 3, 3, 2, 4, 4, 5, 3, 1, 4, 5, 5, 6, 6, 7, 4, 6, 7, 2, 5, 8, 6, 3, 7, 1, 7, 5, 8, 8, 4, 9, 8, 9, 9, 10, 10, 6, 10, 9, 11, 11, 10, 11, 2, 8, 12, 11, 3, 7, 10, 12, 5, 12, 9, 11, 4, 13, 13, 14, 13, 12, 6, 14, 13, 14, 10, 15, 15, 16, 15, 11, 13

Offset: 1

Author

Neal Gersh Tolunsky, Feb 09 2025

Keywords

• nonn

Comments

A260873 gives the indices of 1s in the sequence.

The longest run in the sequence has length 2.

No three equal terms will appear at indices in arithmetic progression.

For any value k, the distances between pairs of k will be distinct.

Examples

			a(7) = 3: a(7) cannot be 1 because i = 4; i = 1,7; and i = 1,4,7 would all have the same mean index 4. a(7) cannot be 2 because i = 6; i = 5,6,7; and i = 5,7 would have the same mean index 6. So a(7) = 3.
a(19) cannot be 1, 2, or 3. a(19) = 4 does not work either because i = 13,19 would have the same mean (namely 16) as i = 12,17,19. So a(19) = 5.
		

Links

• Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A380783, A380751.