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nonn,easy,base,changed

proposed

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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).

proposed

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proposed

allocated for M. F. Hasler

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

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

0,2

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).

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

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

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

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

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

allocated

nonn,easy,base,changed

M. F. Hasler, Oct 09 2017

approved

editing

allocated for M. F. Hasler

allocated

approved