A189820 a(3*k-2) = a(k), a(3*k-1) = a(k), a(3*k) = 1 for k >= 1, starting with a(1) = 0.

0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1

Comments

Together with A189816, this sequence completes the list of "type 3,3" sequences described at A189628.

Alternate definition: a(n) = 1 if the ternary representation of n-1 has at least one "2" in it. Otherwise, a(n) = 0. Partial sums are given by A081610. - Nathaniel Johnston, May 17 2011

From Gabriele Fici, Mar 10 2024: (Start)

Fixed point of the substitution 0->001, 1->111.

An example of a Rote sequence, that is, it has exactly 2m distinct contiguous subsequences of length m, for every m >= 1. For example, there are 6 contiguous subsequences of length 3, namely 001, 010, 011, 100, 110, 111. (End)

Links

Antti Karttunen, Table of n, a(n) for n = 1..13122

G. Rote, Sequences With Subword Complexity 2n, Journal of Number Theory, Volume 46, Issue 2, February 1994, pp. 196-213.

Index entries for characteristic functions

Mathematica

a[1] = 0; h = 180;
Table[a[3 k - 2] = a[k], {k, 1, h}];
Table[a[3 k - 1] = a[k], {k, 1, h}];
Table[a[3 k] = 1, {k, 1, h}];
Table[a[n], {n, 1, h}]   (* this sequence *)
Flatten[Position[%, 0]]  (* A003278 *)
Flatten[Position[%%, 1]] (* A189822 *)

Prog

(PARI) a(n)=if(n<6, n==3, if(n%3, a(n\3+1), 1)) \\ Charles R Greathouse IV, Aug 11 2011
(Scheme) (define (A189820 n) (cond ((= 1 n) 0) ((zero? (modulo n 3)) 1) (else (A189820 (+ 1 (/ (- n (modulo n 3)) 3)))))) ;; Antti Karttunen, Aug 18 2017

Crossrefs

Cf. A081610, A189628, A003278, A189822.

Sequence in context: A284388 A289174 A059125 * A111406 A353463 A260445

Adjacent sequences: A189817 A189818 A189819 * A189821 A189822 A189823

Keyword

nonn,easy

Author

Clark Kimberling, Apr 28 2011

Extensions

Typo in definition fixed by Reinhard Zumkeller, Aug 11 2011

Status

approved