A051764 - OEIS

This site is supported by donations to The OEIS Foundation.

A051764

Torus knots with n crossings.

0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 0, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 3, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 3, 1, 1, 1, 1, 3, 3 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,15`
	REFERENCES	`Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 1,701,936 Knots." Math. Intell., 20, 33-48, Fall 1998.` `Kunio Murasugi, On the braid index of alternating links, Trans. Amer. Math. Soc. 326 (1991), 237-260.`
	LINKS	`Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.` `R. G. Scharein, Torus knots and links by crossing number` `D. Bar-Natan, 36 Torus Knots(with up to 36 crossings)`
	FORMULA	`a(n) = cardinality of the set {k\| sqrt(n) < k <= n and gcd(k, 1+n/k) = 1}; see Murasugi article. - Hermann Gruber (HermelBraeu(AT)gmx.de), Mar 05 2003`
	CROSSREFS	`Sequence in context: A120936 A173432 A101675 * A025906 A020944 A025897` `Adjacent sequences: A051761 A051762 A051763 * A051765 A051766 A051767`
	KEYWORD	`nonn,nice`
	AUTHOR	`Eric Weisstein (eric(AT)weisstein.com)`

Content is available under The OEIS End-User License Agreement .

Last modified February 13 06:53 EST 2012. Contains 205451 sequences.