A051765 Number of prime satellite knots with n crossings.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 10, 29, 86, 245, 920

Offset

1,13

Comments

Weisstein says that Hoste et al. said that all satellite knots are prime, but actually they didn't say it about all satellite knots; moreover, the conventional definition of satellite knots implies that all composite knots are satellite. - Andrei Zabolotskii, Nov 25 2021

Links

Table of n, a(n) for n=1..20.

Benjamin A. Burton, The next 350 million knots, 36th International Symposium on Computational Geometry (SoCG 2020), Leibniz Int. Proc. Inform., vol. 164, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020, pp. 25:1-25:17. See also knot tables in Supporting Data for Regina.

Jim Hoste, Morwen Thistlethwaite and Jeff Weeks, The First 1,701,936 Knots, Math. Intell., 20, 33-48, Fall 1998.

Andrei Malyutin, On the question of genericity of hyperbolic knots, arXiv preprint arXiv:1612.03368 [math.GT], 2016.

Morwen B. Thistlethwaite, The enumeration and classification of prime 20-crossing knots, Algebraic & Geometric Topology, 25 (2025), 329-344.

Eric Weisstein's World of Mathematics, Hyperbolic Knot

Eric Weisstein's World of Mathematics, Knot

Eric Weisstein's World of Mathematics, Satellite Knot

Crossrefs

Cf. A002863, A051764, A052408, A086825.

Sequence in context: A208900 A229733 A383494 * A265987 A076907 A260785

Adjacent sequences: A051762 A051763 A051764 * A051766 A051767 A051768

Keyword

nonn,nice,more

Author

Eric W. Weisstein

Extensions

a(17)-a(19) from Burton's data added by Andrei Zabolotskii, Nov 25 2021

a(20) from Thistlethwaite (2025) added by Andrei Zabolotskii, Jan 31 2026

Status

approved