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A134022 Number of negative trits in balanced ternary representation of n.

%I A134022 #29 Apr 11 2021 04:51:33
%S A134022 0,0,1,0,0,2,1,1,1,0,0,1,0,0,3,2,2,2,1,1,2,1,1,2,1,1,1,0,0,1,0,0,2,1,
%T A134022 1,1,0,0,1,0,0,4,3,3,3,2,2,3,2,2,3,2,2,2,1,1,2,1,1,3,2,2,2,1,1,2,1,1,
%U A134022 3,2,2,2,1,1,2,1,1,2,1,1,1,0,0,1,0,0,2,1,1,1,0,0,1,0,0,3,2,2,2,1,1,2,1,1,2
%N A134022 Number of negative trits in balanced ternary representation of n.
%D A134022 D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
%H A134022 Reinhard Zumkeller, <a href="/A134022/b134022.txt">Table of n, a(n) for n = 0..10000</a>
%H A134022 Wikipedia, <a href="http://en.wikipedia.org/wiki/Balanced_ternary">Balanced Ternary</a>
%F A134022 a(n) = A134021(n) - A134023(n) - A134024(n).
%F A134022 a(n) = A005812(n) - A134024(n) = A134024(n) - A065363(n).
%e A134022 100 = 1*3^4+1*3^3-1*3^2+0*3^1+1*3^0 == '++-0+': a(100) = 1;
%e A134022 200 = 1*3^5-1*3^4+1*3^3+1*3^2+1*3^1-1*3^0 == '+-+++-': a(200) = 2;
%e A134022 300 = 1*3^5+1*3^4-1*3^3+0*3^2+1*3^1+0*3^0 == '++-0+0': a(300) = 1.
%t A134022 Array[Count[#, -1] &[Prepend[IntegerDigits[#, 3], 0] //. {a___, b_, 2, c___} :> {a, b + 1, -1, c}] &, 105, 0] (* _Michael De Vlieger_, Jun 27 2020 *)
%o A134022 (Python)
%o A134022 def a(n):
%o A134022     s=0
%o A134022     x=0
%o A134022     while n>0:
%o A134022         x=n%3
%o A134022         n=n//3
%o A134022         if x==2:
%o A134022             x=-1
%o A134022             n+=1
%o A134022         if x==-1: s+=1
%o A134022     return s
%o A134022 print([a(n) for n in range(151)]) # _Indranil Ghosh_, Jun 07 2017
%Y A134022 Cf. A059095, A134023, A134024.
%K A134022 nonn,base
%O A134022 0,6
%A A134022 _Reinhard Zumkeller_, Oct 19 2007