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

Author

Reinhard Zumkeller, Oct 19 2007

Keywords

• nonn
• base

Examples

			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.
		

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

Crossrefs

Cf. A059095, A134023, A134024.

Programs

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 *)

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

Formula

a(n) = A134021(n) - A134023(n) - A134024(n).

a(n) = A005812(n) - A134024(n) = A134024(n) - A065363(n).