A127834 Numbers whose 8-bit binary representation, when rotated by up to one bit, contains every 3-bit binary representation for the numbers 0 through 7.

23, 29, 46, 58, 71, 92, 113, 116, 139, 142, 163, 184, 197, 209, 226, 232

Offset

1,1

Comments

The binary representations of these numbers are equivalent under rotation / complement.

When this binary representation, with two bits from one end concatenated to the other, is given as input to an elementary cellular automaton, the first line of output will uniquely identify the rule of the automaton.

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Example

23 has the 8-bit representation 00010111.
Concatenate the last two digits onto the beginning to get 1100010111.
We read off the 3-bit substrings:
110
100
000
001
010
101
011
111

Prog

(Sage)
i = 0
while i < 256:
    bin = i.binary()
    bin = bin[ -2:] + "0"*(8-len(bin)) + bin
    subs = []
    for j in range(8):
        k = bin[j:j+3]
        if k not in subs:
            subs.append(k)
        else: break
    if len(subs) == 8: print(i)
    i += 1

Crossrefs

Sequence in context: A095077 A106989 A106988 * A108111 A085713 A102904

Adjacent sequences: A127831 A127832 A127833 * A127835 A127836 A127837

Keyword

fini,full,nonn

Author

Tomas Boothby, Feb 01 2007

Status

approved