A096271 Ternary sequence that is a fixed point of the morphism 0 -> 01, 1 -> 02, 2 -> 00.

0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0

Offset: 0

Author

N. J. A. Sloane, Jun 23 2004

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences that are fixed points of mappings.

Crossrefs

Cf. A007814, A071858.

Programs

Mathematica

Nest[ Function[ l, {Flatten[(l /. {0 -> {0, 1}, 1 -> {0, 2}, 2 -> {0, 0}})]}], {0}, 7] (* Robert G. Wilson v, Feb 26 2005 *)

PARI

map(d)=if(d==2,[0,0],if(d==1,[0,2],[0,1]))
{m=53;v=[];w=[0];while(v!=w,v=w;w=[];for(n=1,min(m,length(v)),w=concat(w,map(v[n]))));for(n=1,2*m,print1(v[n],","))} \\ Klaus Brockhaus, Jun 23 2004

PARI

A096271(n) = if(!(n%2),0,(1+A096271((n-1)/2))%3); \\ Antti Karttunen, Nov 01 2018

Python

def A096271(n): return (~(n+1) & n).bit_length()%3 # Chai Wah Wu, Jan 09 2023

Formula

Recurrence: a(2n) = 0, a(2n+1) = (a(n)+1) mod 3. - Ralf Stephan, Dec 11 2004

a(n) = A007814(n+1) mod 3. - Gabriele Fici, Mar 28 2019

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4/7. - Amiram Eldar, Jan 11 2023

Extensions

More terms from Klaus Brockhaus, Jun 23 2004