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A064235
The smallest power of 3 that is greater than or equal to n.
6
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
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
(Python)
from gmpy2 import digits
def A064235(n): return 3**len(digits(n-1, 3)) if n>1 else 1 # Chai Wah Wu, Oct 21 2024
CROSSREFS
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