A381856 Lexicographically earliest sequence of positive integers such that for any value k, no two sets of two or more indices at which k occurs have the same standard deviation.

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

Offset: 1

Author

Neal Gersh Tolunsky, Mar 08 2025

Keywords

• nonn

Comments

A382381 gives the indices of 1s in this sequence.

If the definition is modified to compare all sets of indices whose terms are equal (not just those sets with the same value k), we get A337226.

Examples

			a(13) = 3: a(13) cannot be 1 as i = 4,13 would have the same standard deviation as i = 1,4,8,13 (namely 4.5). We cannot have a(13) = 2 because i = 3,6 would have the same standard deviation as i = 10,13 (namely 1.5). With a(13) = 3, we find that no two subsets of i = 7,9,12,13 have the same standard deviation, so a(13) = 3.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A382381, A337226, A380968, A380783, A380751.