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A134024
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Number of positive trits in balanced ternary representation of n.
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6
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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
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OFFSET
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0,5
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, Vol 2, pp 173-175.
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LINKS
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FORMULA
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a(n) > 0 for n > 0.
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EXAMPLE
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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.
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MATHEMATICA
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Array[Count[#, 1] &[Prepend[IntegerDigits[#, 3], 0] //. {a___, b_, 2, c___} :> {a, b + 1, -1, c}] &, 105, 0] (* Michael De Vlieger, Jun 27 2020 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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