A234538 (Number of positive digits of n written in base 3) modulo 3.

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

Offset: 0

Author

Vladimir Shevelev, Jan 13 2014

Keywords

• nonn
• base
• easy

Comments

Since A000120 is the number of positive digits of n written in binary, this sequence is a formal ternary analog of the Thue-Morse sequence A010060. However, one cannot name it a "ternary version of A010060" like the known versions A053838, A071858, A036577-A036586, since it is not "cubefree"; i.e., it contains the same 3 consecutive terms, and there is not a known morphism for which it is a fixed point.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 0..999

Crossrefs

Cf. A000120, A010060, A036577-A036586, A053838, A071858, A160384.

Programs

Mathematica

a[n_] := Mod[Plus @@ DigitCount[n, 3, {1, 2}], 3]; Array[a, 100, 0] (* Amiram Eldar, Jul 24 2023 *)

PARI

a(n)=my(d=digits(n, 3)); sum(i=1, #d, !d[i])%3 \\ Charles R Greathouse IV, Jan 13 2014

Formula

A160384(n) == a(n) (mod 3).