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 A130444 Marking indices for the unique optimal Golomb ruler of order 24. 2
 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; text; internal format)
 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 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: A264512 A231764 A208136 * A177697 A287534 A145849 Adjacent sequences:  A130441 A130442 A130443 * A130445 A130446 A130447 KEYWORD fini,full,nonn AUTHOR Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2007 STATUS approved

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Last modified August 9 12:53 EDT 2020. Contains 336323 sequences. (Running on oeis4.)