A134027 Nonnegative numbers that are palindromes in balanced ternary representation.

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

Offset: 1

Author

Reinhard Zumkeller, Oct 19 2007

Keywords

• nonn
• base

Comments

A134028(a(n)) = a(n).

Examples

			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+'.
		

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

Crossrefs

Cf. A014190.

Programs

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 *)