OFFSET
0,2
COMMENTS
The reduced values are Ms(n) = 0, 1/3, 2/9, 1/9, 4/81, 5/243, 2/243, 7/2187, 8/6561, 1/2187, ... .
Numerators: 0, 1, 2, 1, 4, ... = A038502(n).
Ms(-n) = 0, -3, -18, ... = - A036290(n).
Difference table of Ms(n):
0, 1/3, 2/9, 1/9, 4/81, 5/243, 2/243, ...
1/3, -1/9, -1/9, -5/81, -7/243, -1/81, ...
-4/9, 0, 4/81, 8/243, 4/243, ...
4/9, 4/81, -4/243, -4/243, ...
-32/81, -16/243, 0, ...
80/243, 16/243, ...
-64/243, ...
etc.
The difference table of O(n) = n/2^n (Oresme numbers) has its 0's on the main diagonal. Here the 0's appear every two rows. For n/4^n,they appear every three rows. (The denominators of O(n) are 2^A093048(n)).
All terms are powers of 3 (A000244).
FORMULA
a(3n+1) = 3^(3n+1), a(3n+2) = 3^(3n+2).
a(3n+6) = 27*(3n+3).
From Peter Bala, Feb 25 2019: (Start)
a(n) = 3^n/gcd(n,3^n).
O.g.f.: 1 + F(3*x) - (2/3)*F((3*x)^3) - (2/9)*F((3*x)^9) - (2/27)*F((3*x)^27) - ..., where F(x) = x/(1 - x).
O.g.f. for reciprocals: Sum_{n >= 0} x^n/a(n) = 1 + F((x/3)) + 2*( F((x/3)^3) + 3*F((x/3)^9) + 9*F((x/3)^27) + ... ). Cf. A038502. (End)
MATHEMATICA
Table[Denominator[n/3^n], {n, 0, 28}] (* Michael De Vlieger, Jun 03 2016 *)
PROG
(Sage) [1] + [3^(n-n.valuation(3)) for n in [1..30]] # Tom Edgar, Jun 02 2016
(PARI) a(n) = denominator(n/3^n) \\ Felix Fröhlich, Jun 07 2016
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Paul Curtz, Jun 02 2016
STATUS
approved