A269161 Formula for Wolfram's Rule 86 cellular automaton: a(n) = 4n XOR (2n OR n).

0, 7, 14, 11, 28, 27, 22, 19, 56, 63, 54, 51, 44, 43, 38, 35, 112, 119, 126, 123, 108, 107, 102, 99, 88, 95, 86, 83, 76, 75, 70, 67, 224, 231, 238, 235, 252, 251, 246, 243, 216, 223, 214, 211, 204, 203, 198, 195, 176, 183, 190, 187, 172, 171, 166, 163, 152, 159, 150, 147, 140, 139, 134, 131, 448, 455, 462, 459

Offset

0,2

Comments

The sequence is injective: no value occurs more than once.

Fibbinary numbers (A003714) give all integers n>=0 for which a(n) = A048727(n) and for which a(n) = A269160(n).

Links

Antti Karttunen, Table of n, a(n) for n = 0..16383

Eric Weisstein's World of Mathematics, Rule 30

Index entries for sequences related to cellular automata

Index to Elementary Cellular Automata

Formula

a(n) = 4n XOR (2n OR n) = A003987(4*n, A003986(2*n, n)).

a(n) = 4*n XOR A163617(n).

Other identities. For all n >= 0:

a(2*n) = 2*a(n).

a(n) = A057889(A269160(A057889(n))). [Rule 86 is the mirror image of rule 30.]

Mathematica

a[n_] := BitXor[4n, BitOr[2n, n]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Feb 23 2016 *)

Prog

(Scheme) (define (A269161 n) (A003987bi (* 4 n) (A003986bi (* 2 n) n))) ;; Where A003986bi and A003987bi are implementation of dyadic functions giving bitwise-OR (A003986) and bitwise-XOR (A003987) of their arguments.
(Python)
def A269161(n): return n<<2 ^ (n<<1 |n) # Chai Wah Wu, Jun 29 2022

Crossrefs

Cf. A003714, A003986, A003987, A057889, A163617.

Cf. A265281 (iterates starting from 1).

Cf. also A048727, A269160.

Sequence in context: A048727 A295123 A196178 * A307964 A225556 A064666

Adjacent sequences: A269158 A269159 A269160 * A269162 A269163 A269164

Keyword

nonn

Author

Antti Karttunen, Feb 20 2016

Status

approved