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

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• nice
• more

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. - Andrey Zabolotskiy, Nov 25 2021

Links

• 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.
• 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.

Extensions

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