A267581 - OEIS

%I #25 Jan 31 2023 08:40:30

%S 1,3,6,13,26,53,107,215,430,861,1723,3447,6895,13791,27583,55167,

%T 110334,220669,441339,882679,1765359,3530719,7061439,14122879,

%U 28245759,56491519,112983039,225966079,451932159,903864319,1807728639,3615457279,7230914558

%N Decimal representation of the middle column of the "Rule 167" elementary cellular automaton starting with a single ON (black) cell.

%C 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

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

%H Robert Price, <a href="/A267581/b267581.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%F a(n) = floor(c*2^(n+1)), where c = 0.841789245... - _Lorenzo Sauras Altuzarra_, Jan 03 2023

%t 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 *)

%Y Cf. A000051, A267576.

%K nonn,easy

%O 0,2

%A _Robert Price_, Jan 17 2016