A239308 Size of smallest set S of integers such that {0,1,2,...,n} is a subset of S-S, where S-S={abs(i-j) | i,j in S}.

1, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10

Offset

0,2

Comments

S need not be a subset of {0,1,2,...,n}, unlike the definition in A046693.

References

J. Leech, On the representation of 1,2,...,n by differences, J. London Math. Soc. 31 (1956) 160-169.

Links

Table of n, a(n) for n=0..37.

Example

a(18)=7 since all integers in {0,1,2...18} are differences of elements of {0,6,9,10,17,22,24}, but not of any 6-element set.
In other words, {0,6,9,10,17,22,24} is an unrestricted difference basis w.r.t. A005488(7)=18.

Crossrefs

A005488, A046693

Sequence in context: A301640 A061420 A003057 * A216256 A309407 A046693

Adjacent sequences: A239305 A239306 A239307 * A239309 A239310 A239311

Keyword

nonn

Author

Steven Finch, Mar 18 2014

Status

approved