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A185169
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Cantor's ordering of positive rational numbers, where a(n) is the balanced ternary representation of the "factorization" of the positive rational number into terms of A186285.
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3
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0, 2, 1, 20, 10, 20001, 21, 12, 10002, 200, 100, 22, 201, 20011, 10022, 102, 11, 2000, 210, 120, 1000, 20000, 2001, 10202, 20101, 1002, 10000, 20000000010, 2010, 1020, 10000000020, 202, 20000000011, 20010, 12002, 122, 211, 21001, 10020, 10000000022, 101, 200000, 2100, 1200, 100000, 20021, 200001, 212, 20000010012, 20100, 2011, 1022, 10200, 10000020021, 121, 100002, 10012
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OFFSET
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1,2
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COMMENTS
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The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
The "factorization" of positive rational numbers into prime powers of the form p^(3^k), k >= 0, (A186285) and their multiplicative inverses, allows each of those prime powers and their multiplicative inverses to be used at most once, since this corresponds to the balanced ternary representation of the exponents of the prime powers p^a and their multiplicative inverses of the prime factorization of positive rational numbers.
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LINKS
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EXAMPLE
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The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
n num+den Factors from A186285 Balanced ternary representation
1 2 1 / 1 Empty product 0
2 3 1 / 2 (1/2) 2
3 3 2 / 1 2 1
4 4 1 / 3 (1/3) 20
5 4 3 / 1 3 10
6 5 1 / 4 (1/8)*2 20001
7 5 2 / 3 (1/3)*2 21
8 5 3 / 2 3*(1/2) 12
9 5 4 / 1 8*(1/2) 10002
10 6 1 / 5 (1/5) 200
11 6 5 / 1 5 100
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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