1,5

Ortho Smith and Stuart Rankin, with coding by Peter de Vries, calculated a(21) = 990623857 on a Compaq ES 45 in just under 14 hours on Jul 01 2003 (Canada Day).

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.

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.

Stuart Rankin, Ortho Smith and John Schermann, Enumerating the Prime Alternating Knots, Part I, Journal of Knot Theory and its Ramifications, 13 (2004), 57-100.

Stuart Rankin, Ortho Smith and John Schermann, Enumerating the Prime Alternating Knots, Part II, Journal of Knot Theory and its Ramifications, 13 (2004), 101-149.

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.

D. Bar-Natan, The Hoste-Thistlethwaite Table of 11 Crossing Knots

S. R. Finch, Knots, links and tangles

Stuart Rankin, Knot Theory Preprints of Ortho Smith and Stuart Rankin

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

University of Western Ontario Student Beowulf Initiative, Project: Prime Knots

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

Cf. A002863. A diagonal of A059739.

Sequence in context: A102226 A058334 A131093 this_sequence A005248 A032102 A100388

Adjacent sequences: A002861 A002862 A002863 this_sequence A002865 A002866 A002867

nonn,hard,nice

njas

Terms from Hoste et al. added by Eric Weisstein (eric(AT)weisstein.com). Further terms from M. B. Thistlethwaite, Feb 10, 2001.

a(20) found by Ortho Smith and Stuart Rankin (srankin(AT)uwo.ca), with coding done by Peter De Vries, Jun 26, 2003

Ortho Smith and Stuart Rankin, with coding by Peter de Vries, calculated a(22) = 4976016485 on an Intel Xeon 2.8ghz in 41.5 hours on Jul 07 2003.

Ortho Flint and Stuart Rankin, with coding by Peter de Vries, calculated a(23) = 25182878921 on a Compaq ES 45 in 228 hours, finishing on Mar 14, 2004