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A110240 Decimal form of binary integer produced by the ON cells at n-th generation following Wolfram's Rule 30 cellular automaton starting from a single ON-cell represented as 1. 13
1, 7, 25, 111, 401, 1783, 6409, 28479, 102849, 456263, 1641433, 7287855, 26332369, 116815671, 420186569, 1865727615, 6741246849, 29904391303, 107568396185, 477630335215, 1725755276049, 7655529137527, 27537575631497 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See A245549 for binary equivalents. See A070952 for number of ON cells. - N. J. A. Sloane, Jul 28 2014

For n > 0: 3 < a(n+1) / a(n) < 5, floor(a(n+1)/a(n)) = A010702(n+1). - Reinhard Zumkeller, Jun 08 2013

Iterates of A269160 starting from a(0) = 1. See also A269168. - Antti Karttunen, Feb 20 2016

Also, the decimal representation of the n-th generation of the "Rule 66847740" 5-neighbors elementary cellular automaton starting with a single ON (black) cell. - Philipp O. Tsvetkov, Jul 17 2019

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Illustration of first 20 generations

Eric Weisstein's World of Mathematics, Rule 30.

FORMULA

From Antti Karttunen, Feb 20 2016: (Start)

a(0) = 1, for n >= 1, a(n) = A269160(a(n-1)).

a(n) = A030101(A265281(n)). [The rule 30 is the mirror image of the rule 86.]

A269166(a(n)) = n for all n >= 0.

(End)

EXAMPLE

a(1)=1 because the automaton begins at first "generation" with one black cell: 1;

a(2)=5 because one black cell, through Rule 30 at 2nd generation, produces three contiguous black cells: 111 (binary), so 7 (decimal);

a(3)=25 because the third generation is "black black white white black" cells: 11001, so 25 (decimal).

MATHEMATICA

rows = 23; ca = CellularAutomaton[30, {{1}, 0}, rows-1]; Table[ FromDigits[ ca[[k, rows-k+1 ;; rows+k-1]], 2], {k, 1, rows}] (* Jean-Fran├žois Alcover, Jun 07 2012 *)

PROG

(Haskell)

a110240 = foldl (\v d -> 2 * v + d) 0 . map toInteger . a070950_row

-- Reinhard Zumkeller, Jun 08 2013

(Scheme, with memoization-macro definec)

(definec (A110240 n) (if (zero? n) 1 (A269160 (A110240 (- n 1)))))

;; Antti Karttunen, Feb 20 2016

CROSSREFS

This sequence, A070952, and A245549 all describe the same sequence of successive states.

Cf. A030101, A070950, A051023, A092539, A092540, A070952 (number of ON cells), A100053, A100054, A100055, A094603, A094604, A000225, A074890, A010702, A245549, A269160, A269162.

Cf. A269165 (indices of ones in this sequence).

Cf. A269166 (a left inverse).

Left edge of A269168.

Cf. also A265281, A269160.

Sequence in context: A155271 A200152 A255280 * A266810 A199893 A129791

Adjacent sequences:  A110237 A110238 A110239 * A110241 A110242 A110243

KEYWORD

easy,nonn,base

AUTHOR

Alexandre Wajnberg and Eric Angelini, Sep 06 2005

EXTENSIONS

More terms from Eric W. Weisstein, Apr 08 2006

Offset corrected by Reinhard Zumkeller, Jun 08 2013

STATUS

approved

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Last modified September 15 20:11 EDT 2019. Contains 327086 sequences. (Running on oeis4.)