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A134027 Nonnegative numbers that are palindromes in balanced ternary representation. 14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A134028(a(n)) = a(n).
REFERENCES
D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
LINKS
Eric Weisstein's World of Mathematics, Palindromic Number
Wikipedia, Balanced Ternary
EXAMPLE
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+'.
MATHEMATICA
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 *)
CROSSREFS
Cf. A014190.
Sequence in context: A182112 A090955 A310683 * A143455 A310684 A087065
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Oct 19 2007
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)