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A064235
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The smallest power of 3 that is greater than or equal to n.
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6
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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MAPLE
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ceil(log(n)/log(3)) ;
3^% ;
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MATHEMATICA
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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 *)
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PROG
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(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])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Sep 22 2001
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EXTENSIONS
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STATUS
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approved
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