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A024629
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n written in fractional base 3/2.
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33
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0, 1, 2, 20, 21, 22, 210, 211, 212, 2100, 2101, 2102, 2120, 2121, 2122, 21010, 21011, 21012, 21200, 21201, 21202, 21220, 21221, 21222, 210110, 210111, 210112, 212000, 212001, 212002, 212020, 212021, 212022, 212210, 212211, 212212, 2101100, 2101101
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OFFSET
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0,3
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COMMENTS
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The number of positive even n such that a(n) has k+1 digits is A005428(k). - Glen Whitney, Jul 09 2017
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LINKS
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Matvey Borodin, Hannah Han, Kaylee Ji, Tanya Khovanova, Alexander Peng, David Sun, Isabel Tu, Jason Yang, William Yang, Kevin Zhang, and Kevin Zhao, Variants of Base 3 over 2, arXiv:1901.09818 [math.NT], 2019.
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FORMULA
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To represent a number in base b, if a digit is >= b, subtract b and carry 1. In fractional base a/b, subtract a and carry b.
a(0)=0, a(3n+r) = 10*a(2n)+r for n >= 0 and r = 0, 1, 2. - Jianing Song, Oct 15 2022
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EXAMPLE
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Representations of the first few numbers are:
0 = 0
1 = 1
2 = 2
3 = 2 0
4 = 2 1
5 = 2 2
6 = 2 1 0
7 = 2 1 1
8 = 2 1 2
9 = 2 1 0 0
10 = 2 1 0 1
11 = 2 1 0 2
12 = 2 1 2 0
13 = 2 1 2 1
14 = 2 1 2 2
15 = 2 1 0 1 0
[extended and reformatted by Peter Munn, Jun 27 2020]
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MAPLE
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a:= proc(n) `if`(n<1, 0, irem(n, 3, 'q')+a(2*q)*10) end:
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MATHEMATICA
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a[ n_] := If[ n < 1, 0, a[ Quotient[n, 3] 2] 10 + Mod[ n, 3]]; (* Michael Somos, Jun 18 2014 *)
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PROG
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(Sage)
def basepqExpansion(p, q, n):
L, i = [n], 1
while L[i-1] >= p:
x=L[i-1]
L[i-1]=x.mod(p)
L.append(q*(x//p))
i+=1
L.reverse()
return Integer(''.join(str(x) for x in L))
(PARI) {a(n) = if( n<1, 0, a(n\3 * 2) * 10 + n%3)}; /* Michael Somos, Jun 18 2014 */
(Haskell)
a024629 0 = 0
a024629 n = 10 * a024629 (2 * n') + t where (n', t) = divMod n 3
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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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EXTENSIONS
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STATUS
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approved
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