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

%I A108964 #16 Sep 03 2021 14:06:49
%S A108964 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,
%T A108964 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,
%U A108964 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
%N A108964 Write n in balanced ternary notation, omit any zeros and form the left-to-right alternating sum mod 3.
%C A108964 This sequence and A036581 are squarefree (they do not contain any substring XX).
%C A108964 Appears to be A307672(n) mod 3. - _Peter Munn_, Aug 22 2021
%H A108964 Alois P. Heinz, <a href="/A108964/b108964.txt">Table of n, a(n) for n = 0..10000</a>
%e A108964 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; ...
%p A108964 a:= proc(n) local d, i, m, l; m:=n; l:=[];
%p A108964       for i from 0 while m>0 do
%p A108964          d:= irem(m, 3, 'm');
%p A108964          if d=2 then m:=m+1; d:=-1 fi;
%p A108964          if d<>0 then l:=[d, l[]] fi
%p A108964       od;
%p A108964       add(l[i]*(-1)^(i-1), i=1..nops(l)) mod 3
%p A108964     end:
%p A108964 seq(a(n), n=0..105);  # _Alois P. Heinz_, May 11 2015
%t A108964 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]];
%t A108964 a /@ Range[0, 105] (* _Jean-François Alcover_, Nov 18 2020, after _Alois P. Heinz_ *)
%Y A108964 Cf. A036581, A307672.
%K A108964 nonn,base
%O A108964 0,3
%A A108964 _Bill Gosper_, Jul 22 2005
%E A108964 More terms from _Alois P. Heinz_, May 11 2015