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 A353234 #30 Jun 14 2022 01:41:59 %S A353234 32,44,138,226,326,310,409,1138,5265,10499 %N A353234 Maximum length of 2 finite snakes in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments). %C A353234 We start with 2 infinite snakes, and 4 possible directions: up, right, down, left. %C A353234 If on its turn one of the snakes cannot execute an order because that square is occupied, it goes to the next order, and so on. %C A353234 The snakes can be blocked and finish there or can continue infinitely. %C A353234 Which are the longest finite snakes using n instructions for 2 snakes that start in the same square (with n >= 4 because with 3 or fewer instructions are infinite)? %H A353234 Ariel Futoransky, <a href="http://snake.puzzlefun.online/">Snake Program</a>, Snake Program to try the snakes, April 2022 (see bottom animation and label for different options). %H A353234 Rodolfo Kurchan, <a href="http://www.puzzlefun.online/problems">Puzzle Fun</a>, Snake Number Problem, March 2022. %e A353234 4 INSTRUCTIONS %e A353234 URDL: 32 %e A353234 -- 30 31 -- -- -- %e A353234 25 26 32 7 8 -- %e A353234 24 20 2 3 9 13 %e A353234 17 18 1 4 15 14 %e A353234 16 12 6 5 19 21 %e A353234 -- 11 10 29 23 22 %e A353234 -- -- -- 28 27 -- %e A353234 1) Both snakes start in square 1. %e A353234 2) First snake go U = 2, second snake can't go Up. %e A353234 3) First snake goes R = 3. %e A353234 4) Second snake goes R = 4. %e A353234 5) First snake cannot go D, so second snake D = 5. %e A353234 6) First snake cannot go L, so second snake goes L = 6 %e A353234 7) First snake can go U = 7, and second cannot go U. %e A353234 8) First snake can go R = 8, second snake cannot go R. %e A353234 9) First snake can go D = 9, second snake can go D = 10. %e A353234 10) First snake cannot go L, second snake can go L = 11. %e A353234 11) First snake cannot go U, second snake can go U = 12. %e A353234 12) First snake can go R = 13, second snake cannot go R. %e A353234 13) First snake can go D = 14, second snake cannot go D. %e A353234 14) First snake can go L = 15, second snake can go L = 16. %e A353234 And so on. %e A353234 | Instructions that give %e A353234 n | Maximum length | the maximal length %e A353234 -------------------------------------------- %e A353234 4 32 URDL %e A353234 5 44 URDLU %e A353234 6 138 UURDLL %e A353234 7 226 UURDUUL %e A353234 8 326 UURDLUUL %e A353234 9 310 UUUURDUUL %e A353234 10 409 URUDLLDURR %e A353234 11 1138 UDDRDDRDUDL %e A353234 12 5265 URUDRDURDDDL %e A353234 13 10499 UUDRUDDLUULDD %e A353234 Computer solutions found by Giorgio Vecchi. %Y A353234 Cf. A353259, A353060, A352388. %K A353234 nonn,more %O A353234 4,1 %A A353234 _Rodolfo Kurchan_, May 01 2022