The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A073008 Decimal expansion of the Traveling Salesman constant. 3
7, 1, 4, 7, 8, 2, 7, 0, 0, 7, 9, 1, 2, 9, 4, 2, 7, 2, 0, 1, 8, 9, 8, 4, 8, 7, 9, 6, 2, 1, 0, 8, 4, 0, 9, 6, 7, 3, 1, 3, 4, 5, 5, 9, 7, 0, 9, 4, 4, 3, 0, 3, 1, 9, 3, 9, 6, 4, 5, 7, 0, 0, 4, 1, 1, 5, 4, 6, 1, 1, 7, 7, 3, 8, 3, 3, 5, 8, 7, 9, 7, 0, 6, 7, 7, 0, 2, 1, 3, 4, 1, 3, 0, 9, 6, 2, 9, 4, 5, 3, 3, 5, 6, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
From Elijah Beregovsky, Jan 10 2020: (Start)
In 1959 J. Beardwood, J. H. Halton and J. M. Hammersley showed that the shortest tour through N random uniformly distributed points in a bounded plane region of area A approaches K*sqrt(N*A), where K is the Traveling Salesman constant, as N approaches infinity. They also proved that 5/8 <= K < 0.922.
In 2015 S. Steinerberger slightly improved both bounds.
In 1995 P. Moscato and N. G. Norman proved that a plane-filling curve called MNPeano is the shortest tour through the set of points defined by MNPeano and observed that the asymptotic expected length of this curve is given by (4/153)*(1+2*sqrt(2))*sqrt(51)*sqrt(N*A), which is very close to the empirical value of the traveling salesman constant.
(End)
REFERENCES
J. Beardwood, J. H. Halton and J. M. Hammersley, The shortest path through many points, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 55, No. 4, 1959, pp. 299-327.
LINKS
J. M. Steele, Probabilistic and worst case analyses of classical problems of combinatorial optimization in Euclidean space, Mathematics of Operations Research, Vol. 15, No. 4 (Nov., 1990), pp. 749-770.
Stefan Steinerberger, New bounds for the traveling salesman constant, arXiv:1311.6338 [math.PR], 2013-2014.
Eric Weisstein's World of Mathematics, Traveling Salesman Constants
FORMULA
Conjectured to be equal to (4/153)*(1+2*sqrt(2))*sqrt(51).
EXAMPLE
0.7147827007912942720189848796210840967313...
CROSSREFS
Sequence in context: A199388 A201750 A198825 * A105199 A020791 A367910
KEYWORD
cons,nonn
AUTHOR
Robert G. Wilson v, Aug 03 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 14 15:00 EDT 2024. Contains 373400 sequences. (Running on oeis4.)