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A002863 Number of prime knots with n crossings.
(Formerly M0851 N0323)
0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705 (list; graph; refs; listen; history; text; internal format)



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


C. C. Adams, The Knot Book, Freeman, NY, 2001; see p. 33.

J. H. Conway, An enumeration of knots and links and some of their algebraic properties. 1970. Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) pp. 329-358 Pergamon, Oxford.

Martin Gardner, The Last Recreations, Copernicus, 1997, 67-84.

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.

M. B. Thistlethwaite, Knot tabulations and related topics. Aspects of topology, 1-76, London Math. Soc. Lecture Note Ser., 93, Cambridge Univ. Press, Cambridge-New York, 1985.


Table of n, a(n) for n=1..16.

S. R. Finch, Knots, links and tangles

J. Hoste, M. B. Thistlethwaite and J. Weeks, The First 1,701,936 Knots, Math. Intell., 20, 33-48, Fall 1998.

W. B. R. Lickorish and K. C. Millett, The new polynomial invariants of knots and links, Math. Mag. 61 (1988), no. 1, 3-23.

K. A. Perko, Jr., On the classification of knots, Proc. Amer. Math. Soc., 45 (1974), 262-266.

R. G. Scharein, Number of Prime Links

N. J. A. Sloane, Illustration of initial terms

M. B. Thistlethwaite, Home Page

M. B. Thistlethwaite, Numbers of knots and links with up to 19 crossings

Eric Weisstein's World of Mathematics, Prime Knot.

Eric Weisstein's World of Mathematics, Knot.

Eric Weisstein's World of Mathematics, Prime Link


Cf. A002864, A086825.

Sequence in context: A080021 A032313 A032223 * A047693 A212265 A107108

Adjacent sequences:  A002860 A002861 A002862 * A002864 A002865 A002866




N. J. A. Sloane.


This is stated incorrectly in CRC Standard Mathematical Tables and Formulae, 30th ed., first printing, 1996, p. 320.

Terms from Hoste et al. added by Eric W. Weisstein



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Last modified July 27 23:23 EDT 2015. Contains 260049 sequences.