A096271 - OEIS

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

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OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences that are fixed points of mappings.

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

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A007814, A071858.

Sequence in context: A202523 A215935 A270573 * A285640 A231189 A363857

Adjacent sequences: A096268 A096269 A096270 * A096272 A096273 A096274

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 23 2004

EXTENSIONS

More terms from Klaus Brockhaus, Jun 23 2004

STATUS

approved