

A186286


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


4



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
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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(2n)) 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(2n)) (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



