A186287 a(n) is the denominator of the rational number whose "factorization" into terms of A186285 has the balanced ternary representation corresponding to n.

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

Offset

0,3

Comments

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).

Links

Daniel Forgues, Table of n, a(n) for n = 0..9841

OEIS Wiki, Orderings of rational numbers

Formula

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).

Example

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

Crossrefs

Cf. A186285, A186286, A185169, A052330.

Sequence in context: A172400 A226691 A158389 * A318393 A340128 A139622

Adjacent sequences: A186284 A186285 A186286 * A186288 A186289 A186290

Keyword

nonn,frac

Author

Daniel Forgues, Feb 17 2011

Status

approved