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A267581 Decimal representation of the middle column of the "Rule 167" elementary cellular automaton starting with a single ON (black) cell. 1
1, 3, 6, 13, 26, 53, 107, 215, 430, 861, 1723, 3447, 6895, 13791, 27583, 55167, 110334, 220669, 441339, 882679, 1765359, 3530719, 7061439, 14122879, 28245759, 56491519, 112983039, 225966079, 451932159, 903864319, 1807728639, 3615457279, 7230914558 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Assuming the conjecture that the positions of the 0-bits of the middle column ("Rule 167") are given by the sequence A000051, it follows that a possible formula could be: a(n) = 2*a(n-1) + 1 - floor((1/2)^((2^(n+1)) mod n)) with a(0)=1 and a(1)=3 (Not proved, but tested up to n = 10^4). - Andres Cicuttin, Mar 29 2016

REFERENCES

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

LINKS

Robert Price, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

S. Wolfram, A New Kind of Science

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

MATHEMATICA

rule=167; rows=20; ca=CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}]; (* Start with single black cell *) catri=Table[Take[ca[[k]], {rows-k+1, rows+k-1}], {k, 1, rows}]; (* Truncated list of each row *) mc=Table[catri[[k]][[k]], {k, 1, rows}]; (* Keep only middle cell from each row *) Table[FromDigits[Take[mc, k], 2], {k, 1, rows}]  (* Binary Representation of Middle Column *)

CROSSREFS

Cf. A000051, A267576.

Sequence in context: A072762 A081254 A125049 * A320733 A164991 A213255

Adjacent sequences:  A267578 A267579 A267580 * A267582 A267583 A267584

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jan 17 2016

STATUS

approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)