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A134027
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Nonnegative numbers that are palindromes in balanced ternary representation.
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14
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0, 1, 4, 7, 10, 13, 16, 28, 40, 43, 52, 61, 73, 82, 91, 103, 112, 121, 124, 160, 196, 208, 244, 280, 292, 328, 364, 367, 394, 421, 457, 484, 511, 547, 574, 601, 613, 640, 667, 703, 730, 757, 793, 820, 847, 859, 886, 913, 949, 976, 1003, 1039, 1066, 1093, 1096
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OFFSET
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1,3
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COMMENTS
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
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LINKS
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EXAMPLE
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a(10) = 43 = 1*3^4 - 1*3^3 - 1*3^2 - 1*3^1 + 1*3^0 == '+---+';
a(11) = 52 = 1*3^4 - 1*3^3 + 0*3^2 - 1*3^1 + 1*3^0 == '+-0-+';
a(12) = 61 = 1*3^4 - 1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 == '+-+-+';
a(13) = 73 = 1*3^4 + 0*3^3 - 1*3^2 + 0*3^1 + 1*3^0 == '+0-0+'.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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