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.

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

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