

A002863


Number of prime knots with n crossings.
(Formerly M0851 N0323)


44



0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705, 8053393, 48266466, 294130458
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OFFSET

1,5


COMMENTS

Prime knot: a nontrivial knot which cannot (as a composite knot can) be written as the knot sum of two nontrivial knots.  Jonathan Vos Post, Apr 30 2011


REFERENCES

For convenience, many references and links related to the enumeration of knots are collected here, even if they do not explicitly refer to this sequence.
C. C. Adams, The Knot Book, Freeman, NY, 2001; see p. 33.
C. Cerf, Atlas of oriented knots and links, Topology Atlas 3 no. 2 (1998).
Peter R. Cromwell, Knots and Links, Cambridge University Press, 2004, pp. 209211.
Martin Gardner, The Last Recreations, Copernicus, 1997, 6784.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. G. Tait, Scientific Papers, Cambridge Univ. Press, Vol. 1, 1898, Vol. 2, 1900, see Vol. 1, p. 345.
M. B. Thistlethwaite, personal communication.


LINKS

For convenience, many references and links related to the enumeration of knots are collected here, even if they do not explicitly refer to this sequence.
B. Burton, The next 350 million knots, 36th International Symposium on Computational Geometry (SoCG 2020) (S. Cabello, D.Z. Chen, eds.), Leibniz Int. Proc. Inform., vol. 164, Schloss DagstuhlLeibnizZentrum fuer Informatik, 2020, pp. 25:125:17.
Knot Atlas, The Knot Atlas. Includes: The Rolfsen Table of knots with up to 10 crossings, The HosteThistlethwaite Table of 11 Crossing Knots, The Thistlethwaite Link Table, The 36 Torus Knots with up to 36 Crossings, and The Mathematica Package KnotTheory.
K. A. Perko, Jr., Primality of certain knots, In Topology Proceedings, vol. 7, no. 1, pp. 109118. Auburn University Mathematics Department and the Institute for Medicine and Mathematics at Ohio University, 1982.
M. B. Thistlethwaite, Knot tabulations and related topics, Aspects of topology, 176, London Math. Soc. Lecture Note Ser., 93, Cambridge Univ. Press, CambridgeNew York, 1985.
Eric Weisstein's World of Mathematics, Knot.


FORMULA



CROSSREFS



KEYWORD

nonn,hard,more,nice


AUTHOR



EXTENSIONS

This is stated incorrectly in CRC Standard Mathematical Tables and Formulae, 30th ed., first printing, 1996, p. 320.
Consolidated references and links on enumeration of knots into this entry, also created entry for knots in Index to OEIS.  N. J. A. Sloane, Aug 25 2015
a(17)a(19) computed by Benjamin Burton, added by Alex Klotz, Jun 21 2021


STATUS

approved



