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A244040
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Sum of digits of n in fractional base 3/2.
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18
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0, 1, 2, 2, 3, 4, 3, 4, 5, 3, 4, 5, 5, 6, 7, 4, 5, 6, 5, 6, 7, 7, 8, 9, 5, 6, 7, 5, 6, 7, 7, 8, 9, 8, 9, 10, 5, 6, 7, 7, 8, 9, 6, 7, 8, 7, 8, 9, 9, 10, 11, 9, 10, 11, 5, 6, 7, 7, 8, 9, 8, 9, 10, 6, 7, 8, 8, 9, 10, 8, 9, 10, 9, 10, 11, 11, 12, 13, 10, 11, 12, 5
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OFFSET
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0,3
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COMMENTS
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The base 3/2 expansion is unique, and thus the sum of digits function is well-defined.
Fixed point starting with 0 of the two-block substitution a,b -> a,a+1,a+2 for a = 0,1,2,... and b = 0,1,2,.... - Michel Dekking, Sep 29 2022
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LINKS
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FORMULA
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a(0)=0, a(3n+r) = a(2n)+r for n >= 0 and r = 0, 1, 2. - David Radcliffe, Aug 21 2021
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EXAMPLE
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In base 3/2 the number 7 is represented by 211 and so a(7) = 2 + 1 + 1 = 4.
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MATHEMATICA
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a[n_]:= a[n]= If[n==0, 0, a[2*Floor[n/3]] + Mod[n, 3]]; Table[a[n], {n, 0, 85}] (* G. C. Greubel, Aug 20 2019 *)
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PROG
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(Sage)
def base32sum(n):
L, i = [n], 1
while L[i-1]>2:
x=L[i-1]
L[i-1]=x.mod(3)
L.append(2*floor(x/3))
i+=1
return sum(L)
[base32sum(n) for n in [0..85]]
(Haskell)
a244040 0 = 0
a244040 n = a244040 (2 * n') + t where (n', t) = divMod n 3
(Python) a244040 = lambda n: a244040((n // 3) * 2) + (n % 3) if n else 0 # David Radcliffe, Aug 21 2021
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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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