A292681 Rule 6: (000, ..., 111) -> (0, 1, 1, 0, 0, 0, 0, 0), without extending to the right of input bit 0.

0, 3, 6, 4, 12, 13, 8, 8, 24, 27, 26, 24, 16, 17, 16, 16, 48, 51, 54, 52, 52, 53, 48, 48, 32, 35, 34, 32, 32, 33, 32, 32, 96, 99, 102, 100, 108, 109, 104, 104, 104, 107, 106, 104, 96, 97, 96, 96, 64, 67, 70, 68, 68, 69, 64, 64, 64, 67, 66, 64, 64, 65, 64, 64, 192, 195, 198, 196, 204, 205, 200, 200, 216

Offset

0,2

Comments

This is A292680 / 2; the orbit of 1 under A292680 is A266180.

Rule 6 is the smallest rule which is even (otherwise infinitely many bits would be switched on at step 1, for any finite starting value) and nontrivial (i.e., does not lead to extinction nor simple reproduction, possibly shifted left or right, of a single-bit initial state).

In the context of elementary cellular automata, one would usually consider one further bit of output (i.e., the cell which has bit 0 of the input as left neighbor). This leads to A292680 which has all terms even, so it is natural to consider this variant.

Links

Table of n, a(n) for n=0..72.

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Example

     n        |         a(n)
   0 =   0[2] |      0[2] =  0
   1 =   1[2] |     11[2] =  3 (bits below 001 and 01(0) are on)
   2 =  10[2] |    110[2] =  6 (1 below 001 and 010, 0 below 10(0))
   3 =  11[2] |    100[2] =  4 (1 below 001, 0 below 011 and 11(0))
   4 = 100[2] |   1100[2] = 12 (as n = 1 and n = 2, shifted right once more)
   5 = 101[2] |   1101[2] = 13 (1 below 001 and 010 (twice), 0 below 101)
   6 = 110[2] |   1000[2] =  8 (as n = 3, shifted right once)
   7 = 111[2] |   1000[2] =  8 (1 below 001, 0 below 011, 111 and 11(0)).

Prog

(PARI) apply( A292681(n, r=6)=sum(i=0, logint(!n+n<<=1, 2)+1, bittest(r, (n>>i)%8)<<i), [0..60])

Crossrefs

Cf. A292680, A266178, A266179, A266180, A019590.

Sequence in context: A098383 A328637 A162523 * A299211 A067979 A091808

Adjacent sequences: A292678 A292679 A292680 * A292682 A292683 A292684

Keyword

nonn,easy

Author

M. F. Hasler, Oct 09 2017

Status

approved