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 A326413 #92 Dec 21 2024 13:38:34 %S A326413 0,0,1,0,1,0,1,1,2,2,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,2,1,1,0,1,1,1,1, %T A326413 1,1,0,1,1,1,0,2,2,1,1,0,2,3,2,2,1,3,1,1,1,1,1,2,2,3,2,3,1,4,3,5,6,1, %U A326413 1,1,1,1,3,1,1,1,3,1,1,0,1,1,1,1,1,1,1,1,2,0,0,1,1,0,0,1,0,1,1,1,0,1,0 %N A326413 Successive squares visited by a knight on the single-digit square spiral, with ties resolved towards the left. %C A326413 Take the standard counterclockwise square spiral starting at 0, as in A304586, but only write one digit at a time in the cells of the spiral: 0,1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,... %C A326413 Place a chess knight at cell 0. Move it to the lowest-numbered cell it can attack, and if there is a tie, move it to the cell closest (in Euclidean distance) to the start, and if there is still a tie, move to the left(*). %C A326413 No cell can be visited more than once. %C A326413 Inspired by the Trapped Knight video and A316667. %C A326413 Just as for A316667, the sequence is finite. After a while, the knight has no unvisited squares it can reach, and the sequence ends with a(1217) = 4. %C A326413 (*)Moving to the left means choose the point with the lowest x-coordinate. This leads to an unambiguous choice of tied squares only for the 'move left' case. %H A326413 Luca Petrone, <a href="/A326413/b326413.txt">Table of n, a(n) for n = 1..1217</a> %H A326413 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2019/05/kneils-knumberphile-knight.html">Kneil's Knumberphile Knight</a>, Cinquante signes, May 04 2019. %H A326413 Eric Angelini, <a href="/A326918/a326918.pdf">Kneil's Knumberphile Knight</a>, Cinquante signes, May 04 2019. [Cached copy, pdf file, with permission] %H A326413 M. F. Hasler, <a href="/wiki/Knight_tours">Knight tours</a>, OEIS wiki, Nov. 2019. %H A326413 N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019). %e A326413 The digit-square spiral is %e A326413 . %e A326413 . %e A326413 2---2---2---1---2---0---2 2 %e A326413 | | | %e A326413 3 1---2---1---1---1 9 3 %e A326413 | | | | | %e A326413 2 3 4---3---2 0 1 1 %e A326413 | | | | | | | %e A326413 4 1 5 0---1 1 8 3 %e A326413 | | | | | | %e A326413 2 4 6---7---8---9 1 0 %e A326413 | | | | %e A326413 5 1---5---1---6---1---7 3 %e A326413 | | %e A326413 2---6---2---7---2---8---2---9 %Y A326413 Cf. A304586, A316667, A328698. %Y A326413 Cf. A326916, A326918; A316328; A326924, A326922; A328908, A328928; A328909, A328929. %K A326413 nonn,fini,full %O A326413 1,9 %A A326413 _N. J. A. Sloane_, Oct 17 2019 %E A326413 More terms from _Luca Petrone_ %E A326413 Corrected and extended by _Eric Angelini_, Oct 24 2019