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.
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
Offset: 1
Keywords
Examples
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; ...
Links
- Rémy Sigrist, C program for A317530
Crossrefs
Cf. A100053.
Programs
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C
See Links section.
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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}]
Extensions
a(30)-a(36) from Robert G. Wilson v, Aug 07 2018
Data corrected and more terms from Rémy Sigrist, Jul 06 2020
Comments