A134023 Number of zeros in balanced ternary representation of n.

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

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