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A186287
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a(n) is the denominator of the rational number whose "factorization" into terms of A186285 has the balanced ternary representation corresponding to n.
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5
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1, 1, 2, 1, 1, 6, 3, 3, 2, 1, 1, 2, 1, 1, 30, 15, 15, 10, 5, 5, 10, 5, 5, 6, 3, 3, 2, 1, 1, 2, 1, 1, 6, 3, 3, 2, 1, 1, 2, 1, 1, 105, 105, 105, 35, 35, 35, 35, 35, 35, 21, 21, 21, 7, 7, 7, 7, 7, 7, 21, 21, 21, 7, 7, 7, 7, 7, 7, 15, 15, 15, 5, 5, 5, 5, 5, 5, 3, 3, 3, 1, 1, 1, 1, 1, 1, 3, 3, 3
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OFFSET
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0,3
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COMMENTS
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Denominators from the ordering of positive rational numbers by increasing balanced ternary representation of the "factorization" of positive rational numbers into terms of A186285 (prime powers with a power of three as exponent).
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LINKS
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Daniel Forgues, Table of n, a(n) for n = 0..9841
OEIS Wiki, Orderings of rational numbers
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FORMULA
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The balanced ternary representation of n
n = Sum(i=0..1+floor(log_3(2|n|)) n_i * 3^i, n_i in {-1,0,1},
is taken as the representation of the "factorization" of the positive rational number c(n)/d(n) into terms from A186285
c(n)/d(n) = Prod(i=0..1+floor(log_3(2|n|)) (A186285(i+1))^(n_i), where A186285(i+1) is the (i+1)th prime power with exponent being a power of 3. Then a(n) is the denominator, i.e., d(n).
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EXAMPLE
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The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
n BalTern A186286/A186287 (in reduced form)
0 0 Empty product = 1 = 1/1, a(n) = 1
1 1 2 = 2/1, a(n) = 1
2 12 3*(1/2) = 3/2, a(n) = 2
3 10 3 = 3/1, a(n) = 1
4 11 3*2 = 6 = 6/1, a(n) = 1
5 122 5*(1/3)*(1/2) = 5/6, a(n) = 6
6 120 5*(1/3) = 5/3, a(n) = 3
7 121 5*(1/3)*2 = 10/3, a(n) = 3
... ...
41 12222 8*(1/7)*(1/5)*(1/3)*(1/2) = 8/210 = 4/105, a(n) = 105
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CROSSREFS
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Cf. A186285, A186286, A185169, A052330.
Sequence in context: A172400 A226691 A158389 * A318393 A340128 A139622
Adjacent sequences: A186284 A186285 A186286 * A186288 A186289 A186290
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KEYWORD
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nonn,frac
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AUTHOR
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Daniel Forgues, Feb 17 2011
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STATUS
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approved
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