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 A319606 a(n) is that generation of the rule-30 1D cellular automaton started from a single ON cell in which n successive OFF cells appears for the first time after a(n-1). 1
 1, 4, 5, 9, 11, 21, 34, 45, 51, 88, 106, 131, 137, 158, 193, 251, 517, 772, 1029, 1283, 1539, 1794, 2052, 2305, 2561, 4101, 5121, 8197, 10241, 12291, 16388, 20482, 32772, 36865, 49154, 57345, 65539, 262150, 294913, 786437, 851969, 1310724, 1441793, 1835011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS OFF cells outside the triangle of active cells are ignored. LINKS Table of n, a(n) for n=0..43. Rémy Sigrist, C program for A319606 EXAMPLE The Rule-30 1D cellular automaton started from a single ON (.) cell generates the following triangle: 1 . 2 . . . 3 . . 0 0 . 4 . . 0 . . . . 5 . . 0 0 . 0 0 0 . 6 . . 0 . . . . 0 . . . 7 . . 0 0 . 0 0 0 0 . 0 0 . 8 . . 0 . . . . 0 0 . . . . . . 9 . . 0 0 . 0 0 0 . . . 0 0 0 0 0 . 10 . . 0 . . . . 0 . . 0 0 . 0 0 0 . . . 11 . . 0 0 . 0 0 0 0 . 0 . . . . 0 . . 0 0 . 12 . . 0 . . . . 0 0 . . 0 . 0 0 0 0 . 0 . . . . 13 . . 0 0 . 0 0 0 . . . 0 0 . . 0 0 . . 0 . 0 0 0 . 0 OFF cell appears for the first time in generation (line) 1, thus a(0) = 1; 1 consecutive OFF cells (0) appear for the first time after line 1 in generation (line) 4, thus a(1) = 4; 2 consecutive OFF cells (00) appear for the first time after (line) 4 in generation (line) 5, thus a(2) = 5. [Corrected by Rémy Sigrist, Jul 06 2020] MATHEMATICA CellularAutomaton[30, {{1}, 0}, 20000]; (Reverse[Internal`DeleteTrailingZeros[ Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %; ls = Table[ Max[Differences[Position[Flatten@{1, %[[n]], 1}, 1]]] - 1, {n, 1, 20000}]; res = {1}; Table[Position[ls, n] // Flatten, {n, 100}]; For[n = 1, n < 40, n++, AppendTo[res, (Select[%[[n]], # > Last[res] &, 1][[1]])]] res PROG (C) See Links section. CROSSREFS Cf. A317530. Sequence in context: A024821 A059610 A341783 * A230239 A194154 A297291 Adjacent sequences: A319603 A319604 A319605 * A319607 A319608 A319609 KEYWORD nonn AUTHOR Philipp O. Tsvetkov, Sep 24 2018 EXTENSIONS Data corrected and more terms from Rémy Sigrist, Jul 06 2020 STATUS approved

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Last modified September 10 16:14 EDT 2024. Contains 375790 sequences. (Running on oeis4.)