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 A317530 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. 2
 4, 3, 5, 7, 9, 17, 45, 33, 44, 67, 47, 66, 130, 65, 129, 517, 260, 516, 259, 515, 258, 514, 257, 513, 4101, 1025, 4100, 2049, 4099, 16388, 4098, 16387, 4097, 16386, 8193, 16385, 262150, 32769, 262149, 65537, 262148, 131073, 262147, 524291, 262146, 524290, 262145, 524289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS OFF cells outside the triangle of active cells are ignored. This is also the position at which n appears for the first time in A100053. LINKS Rémy Sigrist, C program for A317530 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 . 1 OFF cell (0) appears for the first time in generation (line) 4, thus a(1) = 4; 2 consecutive OFF cells (00) appear for the first time in generation (line) 3, thus a(2) = 3; 5 consecutive OFF cells (00000) appear for the first time in generation (line) 9, thus a(5) = 9; ... MATHEMATICA CellularAutomaton[30, {{1}, 0}, 10000]; (Reverse[Internal`DeleteTrailingZeros[       Reverse[Internal`DeleteTrailingZeros[#]]]]) & /@ %; Table[Position[(Max@FoldList[If[#2 == 0, #1 + 1, 0] &, 0, #]) & /@ %, i] //    Flatten // First, {i, 1, 29}] PROG (C) See Links section. CROSSREFS Cf. A100053. Sequence in context: A059902 A304225 A068982 * A171021 A035427 A257120 Adjacent sequences:  A317527 A317528 A317529 * A317531 A317532 A317533 KEYWORD nonn AUTHOR Philipp O. Tsvetkov, Jul 30 2018 EXTENSIONS a(30)-a(36) from Robert G. Wilson v, Aug 07 2018 Data corrected and more terms from Rémy Sigrist, Jul 06 2020 STATUS approved

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Last modified September 18 19:19 EDT 2020. Contains 337172 sequences. (Running on oeis4.)