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A261691
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Change of base from fractional base 3/2 to base 3.
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1
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0, 1, 2, 6, 7, 8, 21, 22, 23, 63, 64, 65, 69, 70, 71, 192, 193, 194, 207, 208, 209, 213, 214, 215, 579, 580, 581, 621, 622, 623, 627, 628, 629, 642, 643, 644, 1737, 1738, 1739, 1743, 1744, 1745, 1866, 1867, 1868, 1881, 1882, 1883, 1887, 1888, 1889, 1929, 1930
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OFFSET
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0,3
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COMMENTS
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To obtain a(n), we interpret A024629(n) as a base 3 representation (instead of base 3/2). More precisely, if A024629(n) = A007089(m), then a(n) = m.
The digits used in fractional base 3/2 are 0,1, and 2, which are the same as the digits used in base 3.
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LINKS
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FORMULA
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For n = Sum_{i=0..m}c_i*(3/2)^i with each c_i in {0,1,2}, a(n) = Sum_{i=0..m}c_i*3^i.
Apparently:
- a(3*n+1) = a(3*n) + 1 for any n >= 0,
- a(3*n+2) = a(3*n+1) + 1 for any n >= 0,
(End)
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EXAMPLE
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The base 3/2 representation of 7 is (2,1,1); i.e., 7 = 2*(3/2)^2 + 1*(3/2) + 1. Since 2*(3^2) + 1*3 + 1*1 = 22, we have a(7) = 22.
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PROG
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(Sage)
def changebase(n):
L=[n]
i=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[i]*3^i for i in [0..len(L)-1]])
[changebase(n) for n in [0..100]]
(PARI) a(n) = { my (v=0, t=1); while (n, v+=t*(n%3); n=(n\3)*2; t*=3); v } \\ Rémy Sigrist, Apr 06 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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