

A233010


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


8



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



