A132171 3^n repeated 3^n times.

1, 3, 3, 3, 9, 9, 9, 9, 9, 9, 9, 9, 9, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81, 81

Offset: 0

Author

Paul Curtz, Nov 04 2007

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A053644, A132162.

Cf. A064235, A000244.

Programs

Haskell

import Data.List (transpose)
a132171 n = genericIndex a132171_list n
a132171_list = 1 : zs where
   zs = 3 : 3 : 3 : (map (* 3) $ concat $ transpose [zs, zs, zs])
-- Reinhard Zumkeller, Sep 01 2015

Maple

seq((3^n)$(3^n),n=0..5); # Robert Israel, Feb 24 2017

Mathematica

Table[ConstantArray[3^n, 3^n], {n, 0, 4}] // Flatten (* or *)
Table[3^Floor@ Log[3, 2 n + 1], {n, 0, 81}] (* Michael De Vlieger, Feb 24 2017 *)

Python

from sympy import integer_log
def A132171(n): return 3**integer_log((n<<1)+1,3)[0] # Chai Wah Wu, Nov 04 2024

Formula

From Robert Israel, Feb 24 2017: (Start)

a(n) = 3^floor(log_3(2n+1)).

a(3*n+1) = a(3*n+2) = a(3*n+3) = 3*a(n).

G.f.: (1-x)^(-1)*Sum_{m>=1} (3^m-3^(m-1))*x^((3^m-1)/2).

(End)

Sum_{n>=0} 1/a(n)^2 = 3/2. - Amiram Eldar, Aug 16 2022