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 A379242 #13 Dec 30 2024 14:53:04 %S A379242 1,3,15,63,189,432,792,1232,1584,2880,4320,5040,6336,7920,12096,15120, %T A379242 19008,22176,30240,33264,43200,47520,44352,65520,75600,108000,90720, %U A379242 120960,168480,131040,151200,181440,252000,196560,221760,237600,362880,403200,302400 %N A379242 Minimum crossing number at which there are n torus knots. %C A379242 Minimum number that can be factored N different ways into p*(q-1) for coprime p and q with p>q. e.g. 63=63*(2-1)=9*(8-1)=21*(4-1); 63 is the smallest crossing number with three torus knots. Odd numbers will admit an alternating (p,2) torus knot with p crossings, all others with q>2 are non-alternating. Based on definition of torus knot and data from A051764. %H A379242 Alexander R. Klotz and Caleb J. Anderson, <a href="https://arxiv.org/abs/2305.17204">Ropelength and writhe quantization of 12-crossing knots</a>, arXiv:2305.17204 [math.GT], 2023; Experimental Mathematics (2024): 1-8. %e A379242 3 = 3*(2-1), 15 = 15*(2-1) = 5*(4-1), 63 = 63*(2-1) = 9*(8-1) = 21*(4-1). %Y A379242 First occurrence of each n in A051764. %K A379242 nonn %O A379242 0,2 %A A379242 _Alex Klotz_, Dec 18 2024 %E A379242 More terms from _Alois P. Heinz_, Dec 29 2024