A382382 Least k for which there exists an n-subset X of {0, ..., k} such that the variances of the subsets of X of size at least 2 are distinct.

0, 1, 3, 6, 11, 17, 27, 48

Offset: 1

Author

Pontus von Brömssen, Mar 23 2025

Keywords

• nonn
• more

Comments

The variance of a nonempty set Y is (Sum_{y in Y} (y-m)^2)/|Y|, where m is the average of Y and |Y| is the size of Y.

0 and a(n) necessarily belong to the set X in the definition.

Examples

			    | a set X that satisfy the condition
  n | (the largest element of X is a(n))
  --+-----------------------------------
  1 | {0}
  2 | {0, 1}
  3 | {0, 1, 3}
  4 | {0, 1, 4,  6}
  5 | {0, 2, 7,  8, 11}
  6 | {0, 1, 4, 10, 12, 17}
  7 | {0, 3, 4, 14, 19, 21, 27}
  8 | {0, 1, 5, 15, 22, 40, 46, 48}
		

Crossrefs

Cf. A003022, A382381, A382383.

Formula

A003022(n) <= a(n) < A382381(n) for n >= 2.