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A292682 Rule 230: (000, ..., 111) -> (0, 1, 1, 0, 0, 1, 1, 1), without extending to the right of input bit 0. 2
0, 3, 6, 5, 12, 15, 10, 11, 24, 27, 30, 29, 20, 23, 22, 23, 48, 51, 54, 53, 60, 63, 58, 59, 40, 43, 46, 45, 44, 47, 46, 47, 96, 99, 102, 101, 108, 111, 106, 107, 120, 123, 126, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The orbit of 1 under this rule is A006977.

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).

LINKS

Table of n, a(n) for n=0..69.

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] |    101[2] =  5  (1 below 001 and 11(0), 0 below 011.)

   4 = 100[2] |   1100[2] = 12  (as n = 1 and n = 2, shifted left once more)

   5 = 101[2] |   1111[2] = 15  (1 below 001, 010 (twice) and 101)

   6 = 110[2] |   1010[2] = 10  (as n = 3, shifted left once)

   7 = 111[2] |   1011[2] = 11  (1 below 001, 111 and 11(0), 0 below 011).

PROG

(PARI) apply( A292682(n, r=230)=sum(i=0, logint(!n+n<<=1, 2)+1, bittest(r, bitand(n>>i, 7))<<i), [0..60])

CROSSREFS

Cf. A006977, A292680, A292681, A266178, A266179, A266180, A019590.

Sequence in context: A246980 A095359 A048724 * A334748 A334079 A328403

Adjacent sequences:  A292679 A292680 A292681 * A292683 A292684 A292685

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Oct 09 2017

STATUS

approved

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Last modified October 22 07:06 EDT 2021. Contains 348160 sequences. (Running on oeis4.)