A283810 Numbers of variables for which the Shapiro inequality holds.

3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19, 21, 23

Offset

1,1

Comments

Given k positive numbers x_1,..., x_k, the inequality

x_1 / (x_2 + x_3) + x_2 / (x_3 + x_4) + ... + x_k / (x_1 + x_2) >= k/2

is known as Shapiro inequality. It has been proved that it holds for every choice of the x's if k <= 12 and k is even or if k <= 23 and k is odd.

Links

Table of n, a(n) for n=1..16.

Wikipedia, Shapiro inequality

Example

The inequality fails for the 14 numbers {2, 92, 1, 97, 4, 99, 9, 96, 11, 91, 10, 88, 6, 88} and thus 14 is not in the sequence.

Crossrefs

Sequence in context: A298113 A026447 A194378 * A130231 A333491 A304816

Adjacent sequences: A283807 A283808 A283809 * A283811 A283812 A283813

Keyword

nonn,full,fini

Author

Giovanni Resta, Mar 17 2017

Status

approved