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 A364240 a(n) is the periodic part (converted to base 10), on the n-th diagonal from the left of rule-30 1-D cellular automaton, when started from a single ON cell. 3
 1, 1, 0, 1, 1, 2, 2, 0, 12, 1, 6, 2, 13, 11, 6, 3, 11, 8, 6, 12, 6, 7, 3, 2, 8, 9, 14, 13, 0, 180, 1, 90, 74, 25, 156, 224, 98, 250, 123, 12, 20, 239, 215, 138, 20, 12, 159, 192, 58, 253, 139, 86, 195, 164, 25, 28, 48, 235, 159, 162, 213, 152, 25, 8, 14, 239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS See A363345 for the periods. LINKS Paolo Xausa, Table of n, a(n) for n = 1..1000 Michael Brunnbauer, Diagonals in elementary cellular automaton 30, 2019 (local PDF copy, with author's permission). Eric S. Rowland, Local Nested Structure in Rule 30, Complex Systems 16 (2006), pp. 239-258. Eric Weisstein's World of Mathematics, Rule 30. Stephen Wolfram, Notes on Chapter 2, Rule 30, from A New Kind of Science Online, Wolfram Media, 2002. Index entries for sequences related to cellular automata EXAMPLE In the following diagram showing the first 22 evolution steps of the CA, three diagonals are highlighted, along with their transient and periodic parts (the rest of the CA is represented by hyphens, for better visualization). . 3rd diagonal __ Transient = 1 - / Repeat = 0 --1 a(3) = 0 --0-- --0---- 12th diagonal --0------ __ Transient = 01 --0--------/ Repeat = 0010 --0--------0- a(12) = 2 --0--------1--- --0--------0----- __ 20th diagonal --0--------0-------/ Transient = 01000101 --0--------1-------0- Repeat = 1100 --0--------0-------1--- a(20) = 12 --0--------0-------0----- --0--------0-------0------- --0--------1-------0--------- --0--------0-------1----------- --0--------0-------0------------- --0--------0-------1--------------- --0--------1-------1----------------- --0--------0-------1------------------- --0--------0-------0--------------------- --0--------0-------0----------------------- --0--------1-------1------------------------- . MATHEMATICA A364240list[nmax_]:=With[{ca=CellularAutomaton[86, {{1}, 0}, {2nmax, {1-nmax, nmax}}]}, Array[FromDigits[Last[FindTransientRepeat[Drop[Diagonal[ca, nmax-#], Ceiling[(#-1)/2]], 2]], 2]&, nmax]]; A364240list[100] CROSSREFS Cf. A070950. Cf. A363344 (diagonals), A363345 (periods), A363346 (length of transients), A364241 (transients). Sequence in context: A335987 A285539 A285783 * A117270 A244137 A354127 Adjacent sequences: A364237 A364238 A364239 * A364241 A364242 A364243 KEYWORD nonn,base AUTHOR Paolo Xausa, Jul 15 2023 STATUS approved

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Last modified November 30 05:42 EST 2023. Contains 367454 sequences. (Running on oeis4.)