A134022 Number of negative trits in balanced ternary representation of n.

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

Offset

0,6

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) - A134023(n) - A134024(n).

a(n) = A005812(n) - A134024(n) = A134024(n) - A065363(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) = 2;
300 = 1*3^5+1*3^4-1*3^3+0*3^2+1*3^1+0*3^0 == '++-0+0': a(300) = 1.

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=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. A059095, A134023, A134024.

Sequence in context: A330166 A081602 A077267 * A262097 A085975 A277778

Adjacent sequences: A134019 A134020 A134021 * A134023 A134024 A134025

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 19 2007

Status

approved