cp's OEIS Frontend

A292682 Rule 230: (000, ..., 111) -> (0, 1, 1, 0, 0, 1, 1, 1), without extending to the right of input bit 0.

%I A292682 #8 Feb 16 2025 08:33:51
%S A292682 0,3,6,5,12,15,10,11,24,27,30,29,20,23,22,23,48,51,54,53,60,63,58,59,
%T A292682 40,43,46,45,44,47,46,47,96,99,102,101,108,111,106,107,120,123,126,
%U A292682 125,116,119,118,119,80,83,86,85,92,95,90,91,88,91,94,93,92,95,94,95,192,195,198,197,204,207
%N A292682 Rule 230: (000, ..., 111) -> (0, 1, 1, 0, 0, 1, 1, 1), without extending to the right of input bit 0.
%C A292682 The orbit of 1 under this rule is A006977.
%C A292682 The substitution rules 000 -> 0 and 100 -> 0 ensure that no (even or odd) input value can ever extend / "propagate" to the right, therefore it is not required to consider the additional digit to the right of input bit 0 (i.e., the cell which would have this bit 0 as left neighbor), as one would usually do in the context of elementary cellular automata (cf., e.g., A292680 vs. A292681).
%H A292682 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A292682 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A292682 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%e A292682      n        |         a(n)
%e A292682    0 =   0[2] |      0[2] =  0
%e A292682    1 =   1[2] |     11[2] =  3  (bits below 001 and 01(0) are on)
%e A292682    2 =  10[2] |    110[2] =  6  (1 below 001 and 010, 0 below 10(0))
%e A292682    3 =  11[2] |    101[2] =  5  (1 below 001 and 11(0), 0 below 011.)
%e A292682    4 = 100[2] |   1100[2] = 12  (as n = 1 and n = 2, shifted left once more)
%e A292682    5 = 101[2] |   1111[2] = 15  (1 below 001, 010 (twice) and 101)
%e A292682    6 = 110[2] |   1010[2] = 10  (as n = 3, shifted left once)
%e A292682    7 = 111[2] |   1011[2] = 11  (1 below 001, 111 and 11(0), 0 below 011).
%o A292682 (PARI) apply( A292682(n,r=230)=sum(i=0,logint(!n+n<<=1,2)+1,bittest(r,bitand(n>>i,7))<<i),[0..60])
%Y A292682 Cf. A006977, A292680, A292681, A266178, A266179, A266180, A019590.
%K A292682 nonn,easy
%O A292682 0,2
%A A292682 _M. F. Hasler_, Oct 09 2017