A283810 - OEIS

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

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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

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

KEYWORD

nonn,full,fini

AUTHOR

STATUS

approved