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A134023 Number of zeros in balanced ternary representation of n. 8
1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

REFERENCES

D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Wikipedia, Balanced Ternary

FORMULA

a(n) = A134021(n) - A134022(n) - A134024(n).

a(n) = A134021(n) - A005812(n).

EXAMPLE

100=1*3^4+1*3^3-1*3^2+0*3^1+1*3^0=='++-0+': a(100)=1;

200=1*3^5-1*3^4+1*3^3+1*3^2+1*3^1-1*3^0=='+-+++-': a(200)=0;

300=1*3^5+1*3^4-1*3^3+0*3^2+1*3^1+0*3^0=='++-0+0': a(300)=2.

MATHEMATICA

Array[Count[If[First@ # == 0, Rest@ #, #], 0] &[Prepend[IntegerDigits[#, 3], 0] //. {a___, b_, 2, c___} :> {a, b + 1, -1, c}] &, 105, 0] (* Michael De Vlieger, Jun 27 2020 *)

PROG

(Python)

def a(n):

    if n==0: return 1

    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

Cf. A005812, A059095, A134021, A134022, A134024.

Sequence in context: A219180 A179952 A321930 * A257931 A325699 A293513

Adjacent sequences:  A134020 A134021 A134022 * A134024 A134025 A134026

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Oct 19 2007

STATUS

approved

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Last modified August 3 10:43 EDT 2021. Contains 346435 sequences. (Running on oeis4.)