A130444 Marking indices for the unique optimal Golomb ruler of order 24.

0, 9, 33, 37, 38, 97, 122, 129, 140, 142, 152, 191, 205, 208, 252, 278, 286, 326, 332, 353, 368, 384, 403, 425

Offset: 1

Author

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

Keywords

• fini
• full
• nonn

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.

Examples

			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.
		

Links

• distributed.net. [ANNOUNCE] OGR-24 Project Complete.
• Hewgill, Greg. With the completion of OGR-24, [...].
• Eric Weisstein's World of Mathematics, Golomb Ruler.

Crossrefs

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.