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A233010 In balanced ternary notation, either a palindrome or becomes a palindrome if trailing 0's are omitted.

%I A233010 #27 Dec 16 2013 12:27:33
%S A233010 0,1,3,4,7,9,10,12,13,16,21,27,28,30,36,39,40,43,48,52,61,63,73,81,82,
%T A233010 84,90,91,103,108,112,117,120,121,124,129,144,156,160,183,189,196,208,
%U A233010 219,243,244,246,252,270,273,280,292,309,324,328,336,351,360,363
%N A233010 In balanced ternary notation, either a palindrome or becomes a palindrome if trailing 0's are omitted.
%C A233010 Symmetric strings of -1, 0, and 1, including as many leading as trailing zeros.
%H A233010 Lei Zhou, <a href="/A233010/b233010.txt">Table of n, a(n) for n = 1..10000</a>
%e A233010 10 is included since in balanced ternary notation 10 = (101)_bt is a palindrome;
%e A233010 144 is included since 144 = (1TT100)_bt, where we use T to represent -1.  When trailing zeros removed, 1TT1 is a palindrome.
%t A233010 BTDigits[m_Integer, g_] :=
%t A233010 Module[{n = m, d, sign, t = g},
%t A233010   If[n != 0, If[n > 0, sign = 1, sign = -1; n = -n];
%t A233010    d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++];
%t A233010    While[Length[t] < d, PrependTo[t, 0]]; t[[Length[t] + 1 - d]] = sign;
%t A233010    t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];
%t A233010 BTpaleQ[n_Integer] := Module[{t, trim = n/3^IntegerExponent[n, 3]},
%t A233010   t = BTDigits[trim, {0}]; t == Reverse[t]];
%t A233010 Select[Range[0, 363], BTpaleQ[#] &]
%Y A233010 Cf. A002113, A061917, A006995, A057890, A134027
%K A233010 nonn,base
%O A233010 1,3
%A A233010 _Lei Zhou_, Dec 13 2013