A134024 Number of positive trits in balanced ternary representation of n.

0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 4, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 4, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 2, 1, 1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 3, 4, 2, 2, 3, 2, 2, 3, 3, 3, 4, 2

Offset

0,5

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) - A134023(n);

a(n) > 0 for n > 0.

a(n) = A005812(n) - A134022(n) = A134022(n) + A065363(n).

Example

100=1*3^4+1*3^3-1*3^2+0*3^1+1*3^0=='++-0+': a(100)=3;
200=1*3^5-1*3^4+1*3^3+1*3^2+1*3^1-1*3^0=='+-+++-': a(200)=4;
300=1*3^5+1*3^4-1*3^3+0*3^2+1*3^1+0*3^0=='++-0+0': a(300)=3.

Mathematica

Array[Count[#, 1] &[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):
    s=0
    x=0
    while n>0:
        x=n%3
        n //= 3
        if x==2:
            x=-1
            n+=1
        if x==1: s+=1
    return s
print([a(n) for n in range(151)]) # Indranil Ghosh, Jun 07 2017

Crossrefs

Cf. A005812, A059095, A065363, A134021, A134022, A134023.

Sequence in context: A088782 A291984 A066672 * A161069 A161108 A161043

Adjacent sequences: A134021 A134022 A134023 * A134025 A134026 A134027

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 19 2007

Status

approved