login
A005812
Weight of balanced ternary representation of n.
(Formerly M0111)
10
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, 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, 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
OFFSET
0,3
COMMENTS
Weight of n means count of nonzero digits of n. - Daniel Forgues, Mar 24 2010
a(n) = A134022(n) + A134024(n) = A134021(n) - A134023(n).
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. Flajolet and Lyle Ramshaw, A note on Gray code and odd-even merge, SIAM J. Comput. 9 (1980), 142-158.
FORMULA
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).
a(n) = Sum_{k>0} floor(|2*sin(n*Pi/3^k)|). - Toshitaka Suzuki, Sep 10 2006
MATHEMATICA
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 *)
PROG
(Lisp) (defun btw (n) (if (= n 0) 0 (multiple-value-bind (q r) (round n 3) (+ (abs r) (btw q)))))
(PARI) a(n)=local(q); if(n<=0, 0, q=round(n/3); abs(n-3*q)+a(q))
(Python)
def a(n):
s=0
x=0
while n>0:
x=n%3
n//=3
if x==2:
x=-1
n+=1
if x!=0: s+=1
return s
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 07 2017
CROSSREFS
Sequence in context: A358134 A205710 A105499 * A362257 A136625 A321861
KEYWORD
easy,nonn,nice
EXTENSIONS
Additional terms from Allan C. Wechsler
STATUS
approved