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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
OFFSET
0,10
REFERENCES
D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
LINKS
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
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Oct 19 2007
STATUS
approved