login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 05:20 EST 2020. Contains 338865 sequences. (Running on oeis4.)