A233010 - OEIS

%I #27 Dec 16 2013 12:27:33

%S 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 84,90,91,103,108,112,117,120,121,124,129,144,156,160,183,189,196,208,

%U 219,243,244,246,252,270,273,280,292,309,324,328,336,351,360,363

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

%C Symmetric strings of -1, 0, and 1, including as many leading as trailing zeros.

%H Lei Zhou, <a href="/A233010/b233010.txt">Table of n, a(n) for n = 1..10000</a>

%e 10 is included since in balanced ternary notation 10 = (101)_bt is a palindrome;

%e 144 is included since 144 = (1TT100)_bt, where we use T to represent -1.  When trailing zeros removed, 1TT1 is a palindrome.

%t BTDigits[m_Integer, g_] :=

%t Module[{n = m, d, sign, t = g},

%t   If[n != 0, If[n > 0, sign = 1, sign = -1; n = -n];

%t    d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++];

%t    While[Length[t] < d, PrependTo[t, 0]]; t[[Length[t] + 1 - d]] = sign;

%t    t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];

%t BTpaleQ[n_Integer] := Module[{t, trim = n/3^IntegerExponent[n, 3]},

%t   t = BTDigits[trim, {0}]; t == Reverse[t]];

%t Select[Range[0, 363], BTpaleQ[#] &]

%Y Cf. A002113, A061917, A006995, A057890, A134027

%K nonn,base

%O 1,3

%A _Lei Zhou_, Dec 13 2013