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

Author

Ben Branman, Jan 30 2011

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

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

Crossrefs

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

Cf. also A269160, A269174, A269175.

Programs

Mathematica

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

Formula

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