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

Lei Zhou, Table of n, a(n) for n = 1..10000

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: A090852 A182112 A090955 * A143455 A087065 A001197

Adjacent sequences:  A134024 A134025 A134026 * A134028 A134029 A134030

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Oct 19 2007

STATUS

approved

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Last modified June 25 11:31 EDT 2017. Contains 288709 sequences.