This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173637 #34 Jan 17 2022 06:10:28 %S A173637 2,4,212,6,33,222,412,3112,232,8,53,422,323,3122,242,21212,211112,612, %T A173637 5112,432,414,4113,3312,32112,3132,31113,252,22212,221112 %N A173637 Conway notation for rational 2-component links. %C A173637 The ordering of the list is based on increasing crossing numbers and inverse lexicographical order for the terms with the same crossing number. %C A173637 This is to links what A122495 is to knots. %C A173637 All these links are chiral. %C A173637 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. %C A173637 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-2). - _Andrey Zabolotskiy_, May 23 2017 %D A173637 C. Cerf, Atlas of oriented knots and links, Topology Atlas 3 no.2 (1998). %D A173637 Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004, p.210. %H A173637 J. H. Conway, <a href="http://www.maths.ed.ac.uk/~aar/papers/conway.pdf">An enumeration of knots and links and some of their algebraic properties</a>, 1970. Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) pp. 329-358 Pergamon, Oxford. %H A173637 C. Giller, <a href="http://dx.doi.org/10.1090/S0002-9947-1982-0642331-X">A family of links and the Conway calculus</a>, Trans. American Math Soc., 270 (1982) 75-109. %H A173637 <a href="/index/K#knots">Index entries for sequences related to knots</a> %e A173637 a(1) = 2 because 2 is the Conway notation for the Hopf link. %e A173637 a(2) = 4 because 4 is the Conway notation for the (2,4) torus link. %Y A173637 Cf. A002863, A002864, A018240, A090597, A122495. %K A173637 nonn %O A173637 1,1 %A A173637 _Jonathan Vos Post_, Nov 23 2010 %E A173637 Sequence edited and more terms added by _Andrey Zabolotskiy_, May 23 2017