A108964 Write n in balanced ternary notation, omit any zeros and form the left-to-right alternating sum mod 3.

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

Offset

0,3

Comments

This sequence and A036581 are squarefree (they do not contain any substring XX).

Appears to be A307672(n) mod 3. - Peter Munn, Aug 22 2021

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

1="1", so a(1)=1; 2=3-1="1,-1", so a(2)=2; 3=3="1,0", so a(3)=1; 4=3+1="1,1", so a(4)=0; ...

Maple

a:= proc(n) local d, i, m, l; m:=n; l:=[];
      for i from 0 while m>0 do
         d:= irem(m, 3, 'm');
         if d=2 then m:=m+1; d:=-1 fi;
         if d<>0 then l:=[d, l[]] fi
      od;
      add(l[i]*(-1)^(i-1), i=1..nops(l)) mod 3
    end:
seq(a(n), n=0..105);  # Alois P. Heinz, May 11 2015

Mathematica

a[n_] := Module[{d, i, m = n, l = {}}, For[i = 0, m>0, i++, d = Mod[m, 3]; m = Quotient[m, 3]; If[d==2, m++; d = -1]; If[d != 0, l = Prepend[l, d]]]; Mod[Sum[l[[i]] (-1)^(i-1), {i, 1, Length[l]}], 3]];
a /@ Range[0, 105] (* Jean-François Alcover, Nov 18 2020, after Alois P. Heinz *)

Crossrefs

Cf. A036581, A307672.

Sequence in context: A141581 A179286 A193690 * A036581 A369462 A135055

Adjacent sequences: A108961 A108962 A108963 * A108965 A108966 A108967

Keyword

nonn,base

Author

Bill Gosper, Jul 22 2005

Extensions

More terms from Alois P. Heinz, May 11 2015

Status

approved