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 A376155 #7 Oct 18 2024 20:33:54 %S A376155 0,1,0,1,6,96,146 %N A376155 Number of prime knots with 10 or fewer crossings whose mosaic number is n. %C A376155 An n X n mosaic is an n X n array of the 11 tiles given by Lomonaco and Kauffman. The mosaic number of a knot K is the smallest integer n such that K is realizable on an n X n knot mosaic. %C A376155 Here, we count the unknot as a prime knot. %H A376155 Aaron Heap, Douglas Baldwin, James Canning, and Greg Vinal, <a href="http://arxiv.org/abs/2303.12138">Tabulating knot mosaics: Crossing number 10 or less</a>, arXiv: 2303.12138 [math.GT], 2023. %H A376155 Hwa Jeong Lee, Ludwig Lewis, Joseph Paat, and Amanda Peiffer, <a href="https://doi.org/10.2140/involve.2018.11.13">Knot mosaic tabulation</a>, Involve, Vol. 11 (2018), pp. 13-26. %H A376155 Samuel J. Lomonaco and Louis H. Kauffman, <a href="http://www.csee.umbc.edu/~lomonaco/pubs/psapm561.pdf">Quantum Knots and Mosaics</a>, Proc. Sympos. Applied Math., Amer. Math. Soc., Vol. 68 (2010), pp. 177-208. %H A376155 <a href="/index/K#knots">Index entries for sequences related to knots</a> %e A376155 There are exactly 6 prime knots that are realizable on a 5 X 5 knot mosaic but not realizable on a 4 X 4 knot mosaic. Namely, these knots are 4_1, 5_1, 5_2, 6_1, 6_2, and 7_4 (see Table 1 of Lee et al.). Hence, a(5) = 6. %Y A376155 Cf. A002863, A374942, A374943, A374944, A374945, A261400, A375353. %K A376155 nonn,fini,full %O A376155 1,5 %A A376155 _Luc Ta_, Sep 12 2024