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 A173637 Conway notation for rational 2-component links. 1
 2, 4, 212, 6, 33, 222, 412, 3112, 232, 8, 53, 422, 323, 3122, 242, 21212, 211112, 612, 5112, 432, 414, 4113, 3312, 32112, 3132, 31113, 252, 22212, 221112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The ordering of the list is based on increasing crossing numbers and inverse lexicographical order for the terms with the same crossing number. This is to links what A122495 is to knots. All these links are cheiral. Each term is actually an ordered set of positive integers, concatenated; as long as all integers are 1-digit, it's not a problem, but a(30) requires "digit" 10, so at that point the sequence becomes not fully well-defined. An irregular array of these numbers would be well-defined. Number of the terms of this sequence with crossing number k plus number of the terms of A122495 with crossing number k equals A005418(k). - Andrey Zabolotskiy, May 23 2017 REFERENCES C. Cerf, Atlas of oriented knots and links, Topology Atlas 3 no.2 (1998). Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004, p.210. LINKS 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. C. Giller, A family of links and the Conway calculus, Trans. American Msth Soc., 270 (1982) 75-109. EXAMPLE a(1) = 2 because 2 is the Conway notation for the Hopf link. a(2) = 4 because 4 is the Conway notation for the (2,4) torus link. CROSSREFS Cf. A002863, A002864, A122495. Sequence in context: A068479 A116010 A018677 * A111355 A018706 A111162 Adjacent sequences:  A173634 A173635 A173636 * A173638 A173639 A173640 KEYWORD nonn AUTHOR Jonathan Vos Post, Nov 23 2010 EXTENSIONS Sequence edited and more terms added by Andrey Zabolotskiy, May 23 2017 STATUS approved

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Last modified October 17 15:32 EDT 2019. Contains 328116 sequences. (Running on oeis4.)