A064235 The smallest power of 3 that is greater than or equal to n.

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

Offset

1,2

Comments

Let A_n be the upper triangular matrix in the group GL(n,3) of invertible n X n matrices over GF(3) that has zero entries below the diagonal and 1 elsewhere. For example for n=4 the matrix is / 1,1,1,1 / 0,1,1,1 / 0,0,1,1 / 0,0,0,1 /. a(n) is the order of this matrix as an element of GL(n,3).

For n>1 a(n) is the smallest integer such that gcd(a(n),2^a(n)+1) >= n. - Benoit Cloitre, Apr 21 2002

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = 3 ^ A080342(n). - Reinhard Zumkeller, Sep 02 2015

Sum_{n>=1} 1/a(n)^2 = 4/3. - Amiram Eldar, Aug 16 2022

Maple

A064235 := proc(n)
        ceil(log(n)/log(3)) ;
        3^% ;
end proc: # R. J. Mathar, Nov 06 2011

Mathematica

nn=100; With[{p3=3^Range[0, Ceiling[Log[3, nn]]]}, Flatten[Table[Select[ p3, #>=n&, 1], {n, nn}]]] (* Harvey P. Dale, Mar 14 2013 *)

Prog

(Haskell)
import Data.List (transpose)
a064235 n = genericIndex a064235_list (n - 1)
a064235_list = 1 : zs where
   zs = 3 : 3 : (map (* 3) $ concat $ transpose [zs, zs, zs])
-- Reinhard Zumkeller, Sep 02 2015

Crossrefs

Cf. A062383.

Cf. A132171, A080342, A000244.

Sequence in context: A347033 A336992 A349673 * A098355 A183429 A107443

Adjacent sequences: A064232 A064233 A064234 * A064236 A064237 A064238

Keyword

nonn

Author

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 22 2001

Extensions

More terms from James A. Sellers, Sep 26 2001

Status

approved