cp's OEIS Frontend

A005812 Weight of balanced ternary representation of n.

%I A005812 M0111 #41 Apr 30 2021 06:07:00
%S A005812 0,1,2,1,2,3,2,3,2,1,2,3,2,3,4,3,4,3,2,3,4,3,4,3,2,3,2,1,2,3,2,3,4,3,
%T A005812 4,3,2,3,4,3,4,5,4,5,4,3,4,5,4,5,4,3,4,3,2,3,4,3,4,5,4,5,4,3,4,5,4,5,
%U A005812 4,3,4,3,2,3,4,3,4,3,2,3,2,1,2,3,2,3,4,3,4,3,2,3,4,3,4,5,4,5,4,3,4,5,4,5,4,3
%N A005812 Weight of balanced ternary representation of n.
%C A005812 Weight of n means count of nonzero digits of n. - _Daniel Forgues_, Mar 24 2010
%C A005812 a(n) = A134022(n) + A134024(n) = A134021(n) - A134023(n).
%D A005812 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005812 Daniel Forgues, <a href="/A005812/b005812.txt">Table of n, a(n) for n = 0..100000</a>
%H A005812 P. Flajolet and Lyle Ramshaw, <a href="http://dx.doi.org/10.1137/0209014">A note on Gray code and odd-even merge</a>, SIAM J. Comput. 9 (1980), 142-158.
%H A005812 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%F A005812 a(3n)=a(n), a(3n+1)=a(n)+1, a(9n+2)=a(n)+2, a(9n+5)=a(3n+2)+1, a(9n+8)=a(3n+2).
%F A005812 a(n) = Sum_{k>0} floor(|2*sin(n*Pi/3^k)|). - _Toshitaka Suzuki_, Sep 10 2006
%t A005812 a[n_] := With[{q=Round[n/3]}, Abs[n-3q]+a[q]]; a[0]=0; Table[a[n], {n, 0, 105}](* _Jean-François Alcover_, Nov 25 2011, after Pari *)
%o A005812 (Lisp) (defun btw (n) (if (= n 0) 0 (multiple-value-bind (q r) (round n 3) (+ (abs r) (btw q)))))
%o A005812 (PARI) a(n)=local(q); if(n<=0,0,q=round(n/3); abs(n-3*q)+a(q))
%o A005812 (Python)
%o A005812 def a(n):
%o A005812     s=0
%o A005812     x=0
%o A005812     while n>0:
%o A005812         x=n%3
%o A005812         n//=3
%o A005812         if x==2:
%o A005812             x=-1
%o A005812             n+=1
%o A005812         if x!=0: s+=1
%o A005812     return s
%o A005812 print([a(n) for n in range(101)]) # _Indranil Ghosh_, Jun 07 2017
%K A005812 easy,nonn,nice
%O A005812 0,3
%A A005812 _N. J. A. Sloane_, _Jeffrey Shallit_
%E A005812 Additional terms from _Allan C. Wechsler_