A005812 Weight of balanced ternary representation of n. (Formerly M0111)

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

Daniel Forgues, Table of n, a(n) for n = 0..100000

P. Flajolet and Lyle Ramshaw, A note on Gray code and odd-even merge, SIAM J. Comput. 9 (1980), 142-158.

Michael Gilleland, Some Self-Similar Integer Sequences

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

Adjacent sequences: A005809 A005810 A005811 * A005813 A005814 A005815

Keyword

easy,nonn,nice

Author

N. J. A. Sloane, Jeffrey Shallit

Extensions

Additional terms from Allan C. Wechsler

Status

approved