|
| |
|
|
A269173
|
|
Formula for Wolfram's Rule 126 cellular automaton: a(n) = (n XOR 2n) OR (n XOR 4n).
|
|
2
|
|
|
|
0, 7, 14, 15, 28, 31, 30, 27, 56, 63, 62, 63, 60, 63, 54, 51, 112, 119, 126, 127, 124, 127, 126, 123, 120, 127, 126, 127, 108, 111, 102, 99, 224, 231, 238, 239, 252, 255, 254, 251, 248, 255, 254, 255, 252, 255, 246, 243, 240, 247, 254, 255, 252, 255, 254, 251, 216, 223, 222, 223, 204, 207, 198, 195, 448, 455, 462
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Antti Karttunen, Table of n, a(n) for n = 0..8191
Eric Weisstein's World of Mathematics, Rule 126
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata
|
|
|
FORMULA
|
a(n) = A048724(n) OR A048725(n) = (n XOR 2n) OR (n XOR 4n), where OR is a bitwise-or (A003986) and XOR is A003987.
Other identities. For all n >= 0:
a(2*n) = 2*a(n).
a(n) = A057889(a(A057889(n))). [Rule 126 is amphichiral (symmetric).]
|
|
|
EXAMPLE
|
a(4) = (4 XOR 2*4) OR (4 XOR 4*4) = 12 OR 20 = 28. - Indranil Ghosh, Apr 02 2017
|
|
|
MATHEMATICA
|
Table[BitOr[BitXor[n, 2n], BitXor[n, 4n]], {n, 0, 100}] (* Indranil Ghosh, Apr 02 2017 *)
|
|
|
PROG
|
(Scheme) (define (A269173 n) (A003986bi (A048724 n) (A048725 n)))
(PARI) for(n=0, 100, print1(bitor(bitxor(n, 2*n), bitxor(n, 4*n)), ", ")) \\ Indranil Ghosh, Apr 02 2017
(Python) print [(n^(2*n))|(n^(4*n)) for n in range(0, 101)] # Indranil Ghosh, Apr 02 2017
(C)
#include <stdio.h>
int main()
{
int n;
for(n=0; n<=100; n++){
printf("%d, ", (n^(2*n))|(n^(4*n)));
}
return 0;
} /* Indranil Ghosh, Apr 02 2017 */
|
|
|
CROSSREFS
|
Cf. A003986, A003987, A048724, A048725, A057889.
Cf. A267365 (iterates starting from 1).
Cf. A269174.
Sequence in context: A173024 A115770 A086779 * A167197 A336797 A100599
Adjacent sequences: A269170 A269171 A269172 * A269174 A269175 A269176
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Antti Karttunen, Feb 22 2016
|
|
|
STATUS
|
approved
|
| |
|
|
