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

1,3

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.

Links

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

Example

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.

Crossrefs

Cf. A380783, A380751.

Sequence in context: A381856 A249337 A316848 * A139124 A024160 A295283

Adjacent sequences: A380965 A380966 A380967 * A380969 A380970 A380971

Keyword

nonn

Author

Neal Gersh Tolunsky, Feb 09 2025

Status

approved