%I #7 Feb 16 2025 08:33:06

%S 0,9,33,37,38,97,122,129,140,142,152,191,205,208,252,278,286,326,332,

%T 353,368,384,403,425

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

%C 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.

%H distributed.net. <a href="http://lists.distributed.net/pipermail/announce/2004/000077.html">[ANNOUNCE] OGR-24 Project Complete</a>.

%H Hewgill, Greg. <a href="http://n0cgi.distributed.net/cgi/planarc.cgi?user=gregh&amp;plan=2004-11-01.23:48">With the completion of OGR-24, [...]</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler</a>.

%e a[5]-a[4] = 1. No other difference from the sequence gives 1.

%e a[10]-a[9] = 2. No other difference from the sequence gives 2.

%e a[5]-a[3] = 5. No other difference from the sequence gives 5.

%e No difference from the sequence gives, for example, 128. See A130445.

%Y 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.

%K fini,full,nonn

%O 1,2

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