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A005812 Weight of balanced ternary representation of n.
(Formerly M0111)
5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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=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: A173964 A205710 A105499 * A136625 A321861 A283431

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

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Last modified April 12 22:36 EDT 2021. Contains 342933 sequences. (Running on oeis4.)