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A130444
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Marking indices for the unique optimal Golomb ruler of order 24.
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2
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0, 9, 33, 37, 38, 97, 122, 129, 140, 142, 152, 191, 205, 208, 252, 278, 286, 326, 332, 353, 368, 384, 403, 425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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. 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.
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LINKS
| distributed.net. [ANNOUNCE] OGR-24 Project Complete.
Hewgill, Greg. With the completion of OGR-24, [...].
Eric Weisstein's World of Mathematics, Golomb Ruler.
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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.
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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.
Sequence in context: A196016 A183426 A061913 * A177697 A145849 A111045
Adjacent sequences: A130441 A130442 A130443 * A130445 A130446 A130447
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KEYWORD
| fini,full,nonn
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AUTHOR
| Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2007
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