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 A353234 Maximum length of 2 finite snakes in the Snake Number Problem with n-periodic instructions in an infinite square grid (see Comments). 2
 32, 44, 138, 226, 326, 310, 409, 1138, 5265, 10499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS We start with 2 infinite snakes, and 4 possible directions: up, right, down, left. 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. The snakes can be blocked and finish there or can continue infinitely. 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)? LINKS Table of n, a(n) for n=4..13. Ariel Futoransky, Snake Program, Snake Program to try the snakes, April 2022 (see bottom animation and label for different options). Rodolfo Kurchan, Puzzle Fun, Snake Number Problem, March 2022. EXAMPLE 4 INSTRUCTIONS URDL: 32 -- 30 31 -- -- -- 25 26 32 7 8 -- 24 20 2 3 9 13 17 18 1 4 15 14 16 12 6 5 19 21 -- 11 10 29 23 22 -- -- -- 28 27 -- 1) Both snakes start in square 1. 2) First snake go U = 2, second snake can't go Up. 3) First snake goes R = 3. 4) Second snake goes R = 4. 5) First snake cannot go D, so second snake D = 5. 6) First snake cannot go L, so second snake goes L = 6 7) First snake can go U = 7, and second cannot go U. 8) First snake can go R = 8, second snake cannot go R. 9) First snake can go D = 9, second snake can go D = 10. 10) First snake cannot go L, second snake can go L = 11. 11) First snake cannot go U, second snake can go U = 12. 12) First snake can go R = 13, second snake cannot go R. 13) First snake can go D = 14, second snake cannot go D. 14) First snake can go L = 15, second snake can go L = 16. And so on. | Instructions that give n | Maximum length | the maximal length -------------------------------------------- 4 32 URDL 5 44 URDLU 6 138 UURDLL 7 226 UURDUUL 8 326 UURDLUUL 9 310 UUUURDUUL 10 409 URUDLLDURR 11 1138 UDDRDDRDUDL 12 5265 URUDRDURDDDL 13 10499 UUDRUDDLUULDD Computer solutions found by Giorgio Vecchi. CROSSREFS Cf. A353259, A353060, A352388. Sequence in context: A308765 A236324 A211813 * A303959 A304602 A305338 Adjacent sequences: A353231 A353232 A353233 * A353235 A353236 A353237 KEYWORD nonn,more AUTHOR Rodolfo Kurchan, May 01 2022 STATUS approved

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