A239308 - OEIS

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

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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

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

KEYWORD

nonn

AUTHOR

Steven Finch, Mar 18 2014

STATUS

approved