A186286 a(n) is the numerator of the rational number whose "factorization" into terms of A186285 has the balanced ternary representation corresponding to n.

1, 2, 3, 3, 6, 5, 5, 10, 5, 5, 10, 15, 15, 30, 7, 7, 14, 7, 7, 14, 21, 21, 42, 7, 7, 14, 7, 7, 14, 21, 21, 42, 35, 35, 70, 35, 35, 70, 105, 105, 210, 4, 8, 16, 4, 8, 16, 12, 24, 48, 4, 8, 16, 4, 8, 16, 12, 24, 48, 20, 40, 80, 20, 40, 80, 60, 120, 240, 4, 8, 16, 4, 8, 16, 12, 24, 48, 4, 8

Offset

0,2

Comments

Numerators 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 numerator, i.e., c(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) = 2
   2     12  3*(1/2) = 3/2,           a(n) = 3
   3     10  3 = 3/1,                 a(n) = 3
   4     11  3*2 = 6 = 6/1,           a(n) = 6
   5    122  5*(1/3)*(1/2) = 5/6,     a(n) = 5
   6    120  5*(1/3) = 5/3,           a(n) = 5
   7    121  5*(1/3)*2 = 10/3,        a(n) = 10
  ...   ...
  41  12222  8*(1/7)*(1/5)*(1/3)*(1/2) = 8/210 = 4/105, a(n) = 4

Crossrefs

Cf. A186285, A186287, A185169, A052330.

Sequence in context: A101447 A119322 A014498 * A023821 A262332 A262240

Adjacent sequences: A186283 A186284 A186285 * A186287 A186288 A186289

Keyword

nonn,frac

Author

Daniel Forgues, Feb 17 2011

Status

approved