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A006895 Parenthesized one way gives the powers of 2: (1), (2), (1+3), ..., another way the powers of 3: (1), (2+1), (3+6), ....

%I A006895 M0158 #12 Oct 09 2013 16:32:36
%S A006895 1,2,1,3,6,2,16,9,23,58,6,128,109,147,512,70,954,1233,815,4096,1650,
%T A006895 6542,13141,3243,32768,23038,42498,131072,3577,258567,272874,251414,
%U A006895 1048576,294333,1802819,2980150,1214154,8388608,4746145,12031071,31015650,2538782
%N A006895 Parenthesized one way gives the powers of 2: (1), (2), (1+3), ..., another way the powers of 3: (1), (2+1), (3+6), ....
%C A006895 Powers of 2 need 1 term or 2 terms parenthesized, whereas powers of 3 need 2 or 3 terms parenthesized, when 3 then the middle term is a power of 2. See A227928. - _Reinhard Zumkeller_, Oct 09 2013
%D A006895 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006895 Reinhard Zumkeller, <a href="/A006895/b006895.txt">Table of n, a(n) for n = 0..1000</a>
%e A006895 .  a(0)                                              =  _^0
%e A006895 .  a(1)                                              =  2^1
%e A006895 .  a(1) + a(2)            =    2 +   1               =  3^1
%e A006895 .  a(2) + a(3)            =    1 +   3        =    4 =  2^2
%e A006895 .  a(3) + a(4)            =    3 +   6        =    9 =  3^2
%e A006895 .  a(4) + a(5)            =    6 +   2        =    8 =  2^3
%e A006895 .  a(6)                                       =   16 =  2^4
%e A006895 .  a(5) + a(6) + a(7)     =    2 +  16 +   9  =   27 =  3^3
%e A006895 .  a(7) + a(8)            =    9 +  23        =   32 =  2^5
%e A006895 .  a(8) + a(9)            =   23 +  58        =   81 =  3^4
%e A006895 .  a(9) + a(10)           =   58 +   6        =   64 =  2^6
%e A006895 .  a(11)                                      =  128 =  2^7
%e A006895 .  a(10) + a(11) + a(12)  =    6 + 128 + 109  =  243 =  3^5
%e A006895 .  a(12) + a(13)          =  109 + 147        =  256 =  2^8
%e A006895 .  a(14)                                      =  512 =  2^9
%e A006895 .  a(13) + a(14) + a(15)  =  147 + 512 +  70  =  3^6 =  729 .
%o A006895 (Haskell)
%o A006895 a006895 n = a006895_list !! n
%o A006895 a006895_list = 1 : f 0 0 (tail a000079_list) (tail a000244_list) where
%o A006895    f x y us'@(u:us) vs'@(v:vs)
%o A006895      | x > 0     = (u - x) : f 0 (u - x + y) us vs'
%o A006895      | y > v - u = (v - y) : f (v + x - y) 0 us' vs
%o A006895      | otherwise =       u : f 0 (u + y) us vs'
%o A006895 -- _Reinhard Zumkeller_, Oct 09 2013
%Y A006895 Cf. A000079, A000244, A006899, A108906, A085239.
%K A006895 nonn,nice
%O A006895 0,2
%A A006895 _N. J. A. Sloane_, K. S. Brown [ kevin2003(AT)delphi.com ]