1,2

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. 1, 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.

distributed.net. [ANNOUNCE] OGR-24 Project Complete.

Hewgill, Greg. With the completion of OGR-24, [...].

Eric Weisstein's World of Mathematics, Golomb Ruler.

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.

Cf. A130445: Integers in [1, 425] not expressible as a difference from this sequence. A130446: Integers in [1, 425] expressible as a difference from this sequence.

Sequence in context: A027620 A051662 A061913 this_sequence A145849 A111045 A020226

Adjacent sequences: A130441 A130442 A130443 this_sequence A130445 A130446 A130447

fini,full,nonn

Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2007