A185169 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.

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

Offset: 1

Author

Daniel Forgues, Feb 19 2011

Keywords

• nonn

Comments

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.

Examples

			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
		

Links

• OEIS Wiki, Cantor ordering of positive rational numbers

Crossrefs

Cf. A020652, A020653, A186285, A186286, A186287, A050376.