A064235 - OEIS

%I #31 Oct 22 2024 07:38:37

%S 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,

%T 27,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,

%U 81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81,81

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

%C 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).

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

%H Reinhard Zumkeller, <a href="/A064235/b064235.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 3 ^ A080342(n). - _Reinhard Zumkeller_, Sep 02 2015

%F Sum_{n>=1} 1/a(n)^2 = 4/3. - _Amiram Eldar_, Aug 16 2022

%p A064235 := proc(n)

%p         ceil(log(n)/log(3)) ;

%p         3^% ;

%p end proc: # _R. J. Mathar_, Nov 06 2011

%t 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 *)

%o (Haskell)

%o import Data.List (transpose)

%o a064235 n = genericIndex a064235_list (n - 1)

%o a064235_list = 1 : zs where

%o    zs = 3 : 3 : (map (* 3) $ concat $ transpose [zs, zs, zs])

%o -- _Reinhard Zumkeller_, Sep 02 2015

%o (Python)

%o from gmpy2 import digits

%o def A064235(n): return 3**len(digits(n-1,3)) if n>1 else 1 # _Chai Wah Wu_, Oct 21 2024

%Y Cf. A062383.

%Y Cf. A132171, A080342, A000244.

%K nonn

%O 1,2

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

%E More terms from _James A. Sellers_, Sep 26 2001