|
Search: id:A127834
|
|
|
| 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. 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. |
|
+0
1
|
|
| 23, 29, 46, 58, 71, 92, 113, 116, 139, 142, 163, 184, 197, 209, 226, 232
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The binary representations of these numbers are equivalent under rotation / complement.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton, MathWorld
|
|
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
|
|
PROGRAM
|
#SAGE code: 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 this_sequence A108111 A085713 A102904
Adjacent sequences: A127831 A127832 A127833 this_sequence A127835 A127836 A127837
|
|
KEYWORD
|
fini,full,nonn
|
|
AUTHOR
|
Tom Boothby (boothby(AT)u.washington.edu), Feb 01 2007
|
|
|
Search completed in 0.002 seconds
|
