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

Author

Tomas Boothby, Feb 01 2007

Keywords

• fini
• full
• nonn

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.

Examples

			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
		

Links

• Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

Programs

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