login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143824 Size of the largest subset {x(1),x(2),...,x(k)} of {1,2,...,n} with the property that all differences |x(i)-x(j)| are distinct. 9
0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A143823 for the number of subsets of {1, 2, ..., n} with the required property.

See A003022 (and A227590) for the values of n such that a(n+1) > a(n). - Boris Bukh, Jul 28 2013

Can be formulated as an integer linear program: maximize sum {i = 1 to n} z[i] subject to z[i] + z[j] - 1 <= y[i,j] for all i < j, sum {i = 1 to n - d} y[i,i+d] <= 1 for d = 1 to n - 1, z[i] in {0,1} for all i, y[i,j] in {0,1} for all i < j. - Rob Pratt, Feb 09 2010

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..500

EXAMPLE

For n = 4, {1, 2, 4} is a subset of {1, 2, 3, 4} with distinct differences 2 - 1 = 1, 4 - 1 = 3, 4 - 2 = 2 between pairs of elements and no larger set has the required property; so a(4) = 3.

CROSSREFS

Cf. A143823, A003002, A003022, A227590.

Sequence in context: A238965 A036042 A162988 * A182009 A034463 A259899

Adjacent sequences:  A143821 A143822 A143823 * A143825 A143826 A143827

KEYWORD

nonn

AUTHOR

John W. Layman, Sep 02 2008

EXTENSIONS

More terms from Rob Pratt, Feb 09 2010

a(41)-a(60) from Alois P. Heinz, Sep 14 2011

More terms and b-file from N. J. A. Sloane, Apr 08 2016 using data from A003022.

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 May 25 19:13 EDT 2019. Contains 323576 sequences. (Running on oeis4.)