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A233010 In balanced ternary notation, either a palindrome or becomes a palindrome if trailing 0's are omitted. 7
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 (list; graph; refs; listen; history; text; internal format)
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 A059010 A066928

Adjacent sequences:  A233007 A233008 A233009 * A233011 A233012 A233013

KEYWORD

nonn,base

AUTHOR

Lei Zhou, Dec 13 2013

STATUS

approved

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Last modified December 7 03:00 EST 2019. Contains 329836 sequences. (Running on oeis4.)