cp's OEIS Frontend

A134028 Reversal of n in balanced ternary representation.

%I A134028 #36 Feb 16 2025 08:33:06
%S A134028 0,1,-2,1,4,-11,-2,7,-8,1,10,-5,4,13,-38,-11,16,-29,-2,25,-20,7,34,
%T A134028 -35,-8,19,-26,1,28,-17,10,37,-32,-5,22,-23,4,31,-14,13,40,-119,-38,
%U A134028 43,-92,-11,70,-65,16,97,-110,-29,52,-83,-2,79,-56,25,106,-101,-20,61,-74,7,88,-47,34,115,-116,-35,46,-89,-8,73,-62,19,100
%N A134028 Reversal of n in balanced ternary representation.
%C A134028 As the graph demonstrates, the sequence makes large negative steps at terms (3^i+1)/2. These steps divide the graph into conspicuous blocks. - _N. J. A. Sloane_, Jul 03 2016
%D A134028 D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
%H A134028 Reinhard Zumkeller, <a href="/A134028/b134028.txt">Table of n, a(n) for n = 0..10000</a>
%H A134028 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Reversal.html">Reversal</a>
%H A134028 Wikipedia, <a href="http://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>
%F A134028 a(A134027(n)) = A134027(n);
%F A134028 A134021(ABS(a(n))) <= A134021(n).
%e A134028 20 = 1*3^3 - 1*3^2 + 1*3^1 - 1*3^0 == '+-+-'
%e A134028 => a(20) = -1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = -20;
%e A134028 21 = 1*3^3 - 1*3^2 + 1*3^1 + 0*3^0 == '+-+0'
%e A134028 => a(21) = 0*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = 7;
%e A134028 22 = 1*3^3 - 1*3^2 + 1*3^1 + 1*3^0 == '+-++'
%e A134028 => a(22) = 1*3^3 + 1*3^2 - 1*3^1 + 1*3^0 = 34;
%e A134028 23 = 1*3^3 + 0*3^2 - 1*3^1 - 1*3^0 == '+0--'
%e A134028 => a(23) = -1*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = -35;
%e A134028 24 = 1*3^3 + 0*3^2 - 1*3^1 + 0*3^0 == '+0-0'
%e A134028 => a(24) = 0*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = -8;
%e A134028 25 = 1*3^3 + 0*3^2 - 1*3^1 + 1*3^0 == '+0-+'
%e A134028 => a(25) = 1*3^3 - 1*3^2 + 0*3^1 + 1*3^0 = 19.
%o A134028 (Python)
%o A134028 def a(n):
%o A134028     if n==0: return 0
%o A134028     s=[]
%o A134028     x=0
%o A134028     while n>0:
%o A134028         x=n%3
%o A134028         n=n//3
%o A134028         if x==2:
%o A134028             x=-1
%o A134028             n+=1
%o A134028         s.append(x)
%o A134028     l=s[::-1]
%o A134028     return sum(l[i]*3**i for i in range(len(l)))
%o A134028 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 10 2017
%Y A134028 Cf. A117966 (balanced ternary representation), A030102, A134021, A274107.
%Y A134028 A134027 gives the numbers whose balanced ternary representation is palindromic.
%K A134028 sign,look,base
%O A134028 0,3
%A A134028 _Reinhard Zumkeller_, Oct 19 2007