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

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, 84, 90, 91, 103, 108, 112, 117, 120, 121, 124, 129, 144, 156, 160, 183, 189, 196, 208, 219, 243, 244, 246, 252, 270, 273, 280, 292, 309, 324, 328, 336, 351, 360, 363

Offset: 1

Author

Lei Zhou, Dec 13 2013

Keywords

• nonn
• base

Comments

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

Examples

			10 is included since in balanced ternary notation 10 = (101)_bt is a palindrome;
144 is included since 144 = (1TT100)_bt, where we use T to represent -1.  When trailing zeros removed, 1TT1 is a palindrome.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113, A061917, A006995, A057890, A134027

Programs

Mathematica

BTDigits[m_Integer, g_] :=
Module[{n = m, d, sign, t = g},
  If[n != 0, If[n > 0, sign = 1, sign = -1; n = -n];
   d = Ceiling[Log[3, n]]; If[3^d - n <= ((3^d - 1)/2), d++];
   While[Length[t] < d, PrependTo[t, 0]]; t[[Length[t] + 1 - d]] = sign;
   t = BTDigits[sign*(n - 3^(d - 1)), t]]; t];
BTpaleQ[n_Integer] := Module[{t, trim = n/3^IntegerExponent[n, 3]},
  t = BTDigits[trim, {0}]; t == Reverse[t]];
Select[Range[0, 363], BTpaleQ[#] &]