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

1,3

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.

Links

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

Example

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.

Crossrefs

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

Sequence in context: A364144 A033666 A281511 * A249337 A316848 A380968

Adjacent sequences: A381853 A381854 A381855 * A381857 A381858 A381859

Keyword

nonn

Author

Neal Gersh Tolunsky, Mar 08 2025

Status

approved