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
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
KEYWORD
nonn,full,fini
AUTHOR
Giovanni Resta, Mar 17 2017
STATUS
approved