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A283810 Numbers of variables for which the Shapiro inequality holds. 0
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 17, 19, 21, 23 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A298113 A026447 A194378 * A130231 A333491 A304816
KEYWORD
nonn,full,fini
AUTHOR
Giovanni Resta, Mar 17 2017
STATUS
approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)