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

0,5

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A130196 A230866 A158209 * A119646 A024693 A025126

Adjacent sequences: A234535 A234536 A234537 * A234539 A234540 A234541

Keyword

nonn,base,easy

Author

Vladimir Shevelev, Jan 13 2014

Status

approved