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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.

%I A185169 #8 Mar 30 2012 17:23:07
%S A185169 0,2,1,20,10,20001,21,12,10002,200,100,22,201,20011,10022,102,11,2000,
%T A185169 210,120,1000,20000,2001,10202,20101,1002,10000,20000000010,2010,1020,
%U A185169 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
%N 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.
%C A185169 The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
%C A185169 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.
%H A185169 OEIS Wiki, <a href="/wiki/Cantor_ordering_of_positive_rational_numbers">Cantor ordering of positive rational numbers</a>
%e A185169 The balanced ternary digits {-1,0,+1} are represented here as {2,0,1}.
%e A185169 n  num+den          Factors from A186285  Balanced ternary representation
%e A185169 1     2      1 / 1     Empty product                  0
%e A185169 2     3      1 / 2     (1/2)                          2
%e A185169 3     3      2 / 1     2                              1
%e A185169 4     4      1 / 3     (1/3)                          20
%e A185169 5     4      3 / 1     3                              10
%e A185169 6     5      1 / 4     (1/8)*2                        20001
%e A185169 7     5      2 / 3     (1/3)*2                        21
%e A185169 8     5      3 / 2     3*(1/2)                        12
%e A185169 9     5      4 / 1     8*(1/2)                        10002
%e A185169 10    6      1 / 5     (1/5)                          200
%e A185169 11    6      5 / 1     5                              100
%Y A185169 Cf. A020652, A020653, A186285, A186286, A186287, A050376.
%K A185169 nonn
%O A185169 1,2
%A A185169 _Daniel Forgues_, Feb 19 2011