A161903 Convert n into a sequence of binary digits, apply one step of the rule 110 cellular automaton, and interpret the results as a binary integer.

0, 3, 6, 7, 12, 15, 14, 13, 24, 27, 30, 31, 28, 31, 26, 25, 48, 51, 54, 55, 60, 63, 62, 61, 56, 59, 62, 63, 52, 55, 50, 49, 96, 99, 102, 103, 108, 111, 110, 109, 120, 123, 126, 127, 124, 127, 122, 121, 112, 115, 118, 119, 124, 127, 126, 125, 104, 107, 110, 111, 100, 103, 98, 97, 192, 195, 198, 199, 204, 207, 206, 205, 216, 219, 222, 223, 220, 223, 218, 217, 240, 243, 246, 247, 252, 255, 254, 253, 248, 251, 254, 255, 244, 247, 242, 241, 224, 227, 230, 231, 236

Offset

0,2

Comments

a(a(a(...1))) (n times) gives A006978(n)

Links

T. D. Noe, Table of n, a(n) for n = 0..1023

Index entries for sequences related to cellular automata

Eric Weisstein's World of Mathematics, Rule 110

Wikipedia, Rule 110

Formula

a(n) = A057889(A269174(A057889(n))). - Antti Karttunen, Jun 02 2018

Example

For n=19, the evolution after one step is
0, 1, 0, 0, 1, 1  (n=19)
1, 1, 0, 1, 1, 1  (a(n)=55)
So a(n)=55.

Mathematica

a[n_] :=
FromDigits[
  Drop[Part[CellularAutomaton[110, {IntegerDigits[n, 2], 0}], 1], -1],
   2]; Table[a[n], {n, 0, 100}]

Crossrefs

Cf. A006978, A070887, A071049, A180001, A186083, A204371.

Cf. also A269160, A269174, A269175.

Sequence in context: A365422 A335431 A269174 * A163617 A189634 A371218

Adjacent sequences: A161900 A161901 A161902 * A161904 A161905 A161906

Keyword

nonn,base

Author

Ben Branman, Jan 30 2011

Status

approved