|
| |
|
|
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
|
|
|
|
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.
|
|
|
KEYWORD
|
fini,full,nonn
|
|
|
AUTHOR
|
Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2007
|
|
|
STATUS
|
approved
|
| |
|
|
