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

1,3

Comments

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

Links

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

Example

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.

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[#] &]

Crossrefs

Cf. A002113, A061917, A006995, A057890, A134027

Sequence in context: A300789 A026225 A026140 * A263488 A344416 A330178

Adjacent sequences: A233007 A233008 A233009 * A233011 A233012 A233013

Keyword

nonn,base

Author

Lei Zhou, Dec 13 2013

Status

approved