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 A366190 #58 Nov 07 2023 04:13:45 %S A366190 4,24,30,34,36,40,42,44,46,48,50,52,54,56,58,60,62,64 %N A366190 Minimal lengths of prime knots formed by orthogonal unit line segments of the cubic lattice. %C A366190 The same term may correspond to more than one knot. For the initial terms, the minimum lengths were found within three layers of the lattice and it is conceivable that the tightest representation of larger knots expand in all three axes. %C A366190 Length 24: 3_1. %C A366190 Length 30: 4_1. %C A366190 Length 34: 5_1. %C A366190 Length 36: 5_2. %C A366190 Length 40: 6_1, 6_2, 6_3. %C A366190 Length 42: 8_19. %C A366190 Length 44: 8_20. %C A366190 Length 46: 7_2, 7_5, 7_6, 8_21. %C A366190 Length 48: 8_3, 8_7, 9_42, 10_124. %C A366190 Length 50: 8_1, 8_2, 8_4, 8_5, 8_6, 8_8, 8_9, 8_10, 8_11, 8_13, 8_14, 8_16, 9_43, 9_44, 9_46, 9_47, 10_139. %C A366190 Length 52: 8_12, 8_15, 8_17, 8_18, 9_45, 9_48, 9_49, 10_132. %C A366190 Length 54: 9_1, 9_3-5, 9_14, 9_19, 9_26, 9_31, 9_40, 9_41, ... . %C A366190 Conjecture: All even numbers >= 40 will appear in this sequence. %H A366190 Andrew Rechnitzer, <a href="https://personal.math.ubc.ca/~andrewr/knots/minimal_knots.html">List of knot data for different cubic lattices</a>. %H A366190 Rob Scharein, Kai Ishihara, Javier Arsuaga, Yuanan Diao, Koya Shimokawa and Mariel Vazquez, <a href="https://iopscience.iop.org/article/10.1088/1751-8113/42/47/475006">Bounds for the minimum step number of knots in the simple cubic lattice</a>, J. Phys. A: Math. Theor. 42 475006 (2009). %H A366190 Thomas Scheuerle, <a href="/A366190/a366190_2.pdf">Examples for a(2) - a(6) with up to 6 crossings</a>. %H A366190 <a href="/index/K#knots">Index entries for sequences related to knots</a> %e A366190 a(1) = 4 because the unknot is represented by four joined unit line segments, forming a closed loop, in the lattice. %e A366190 a(2) = 24 because the second simplest knot, the trefoil knot, 3_1, can be described by 24 joined unit line segments, forming a self-avoiding closed loop in the lattice. %Y A366190 Cf. A122059, A076770. %K A366190 nonn,more %O A366190 1,1 %A A366190 _Tamas Sandor Nagy_ and _Thomas Scheuerle_, Oct 12 2023