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 A134027 Nonnegative numbers that are palindromes in balanced ternary representation. 11

%I

%S 0,1,4,7,10,13,16,28,40,43,52,61,73,82,91,103,112,121,124,160,196,208,

%T 244,280,292,328,364,367,394,421,457,484,511,547,574,601,613,640,667,

%U 703,730,757,793,820,847,859,886,913,949,976,1003,1039,1066,1093,1096

%N Nonnegative numbers that are palindromes in balanced ternary representation.

%C A134028(a(n)) = a(n).

%D D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.

%H Lei Zhou, <a href="/A134027/b134027.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>

%e a(10) = 43 = 1*3^4 - 1*3^3 - 1*3^2 - 1*3^1 + 1*3^0 == '+---+';

%e a(11) = 52 = 1*3^4 - 1*3^3 + 0*3^2 - 1*3^1 + 1*3^0 == '+-0-+';

%e a(12) = 61 = 1*3^4 - 1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 == '+-+-+';

%e a(13) = 73 = 1*3^4 + 0*3^3 - 1*3^2 + 0*3^1 + 1*3^0 == '+0-0+'.

%t balTernDigits[0] := {0}; balTernDigits[n_ /; n > 0] := Module[{unParsed = n, currRem, currExp = 1, digitList = {}, nextDigit}, While[unParsed > 0, If[unParsed == 3^(currExp - 1), digitList = Append[digitList, 1]; unParsed = 0, currRem = Mod[unParsed, 3^currExp]/3^(currExp - 1); nextDigit = Switch[ currRem, 0, 0, 2, -1, 1, 1]; digitList = Append[ digitList, nextDigit]; unParsed = unParsed - nextDigit*3^(currExp - 1)]; currExp++]; digitList = Reverse[digitList]; Return[ digitList]]; balTernDigits[n_ /; n < 0] := (-1) balTernDigits[ Abs[ n]]; palQ[n_] := n == Reverse@ n; Select[ Range@ 1300, palQ@ balTernDigits@# &] (* _Robert G. Wilson v_, Jun 17 2014 *)

%Y Cf. A014190.

%K nonn,base

%O 1,3

%A _Reinhard Zumkeller_, Oct 19 2007

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Last modified April 18 07:59 EDT 2021. Contains 343084 sequences. (Running on oeis4.)