OFFSET
1,2
COMMENTS
By definition of optimal, there is no shorter Golomb ruler of order 24 (that is, a[24]-a[1] = 425 is minimal). Moreover, it is uniquely optimal. By definition of Golomb ruler, each difference from the sequence is unique. That is, for all 1 <= i < j <= 24 with a[j]-a[i] = d, we have a[y]-a[x] = d iff y=j and x=i. J. P. Robinson and A. J. Bernstein discovered this Golomb ruler in 1967. It was verified to be optimal on Nov 01 2004 by a 4-year computation on distributed.net that performed an exhaustive search through 555529785505835800 rulers. This ruler is not perfect because there are values not expressible as a difference of its terms. For these values, see A130445.
LINKS
distributed.net. [ANNOUNCE] OGR-24 Project Complete.
Hewgill, Greg. With the completion of OGR-24, [...].
Eric Weisstein's World of Mathematics, Golomb Ruler.
EXAMPLE
a[5]-a[4] = 1. No other difference from the sequence gives 1.
a[10]-a[9] = 2. No other difference from the sequence gives 2.
a[5]-a[3] = 5. No other difference from the sequence gives 5.
No difference from the sequence gives, for example, 128. See A130445.
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2007
STATUS
approved