A006895 Parenthesized one way gives the powers of 2: (1), (2), (1+3), ..., another way the powers of 3: (1), (2+1), (3+6), .... (Formerly M0158)

1, 2, 1, 3, 6, 2, 16, 9, 23, 58, 6, 128, 109, 147, 512, 70, 954, 1233, 815, 4096, 1650, 6542, 13141, 3243, 32768, 23038, 42498, 131072, 3577, 258567, 272874, 251414, 1048576, 294333, 1802819, 2980150, 1214154, 8388608, 4746145, 12031071, 31015650, 2538782

Offset

0,2

Comments

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

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Example

.  a(0)                                              =  _^0
.  a(1)                                              =  2^1
.  a(1) + a(2)            =    2 +   1               =  3^1
.  a(2) + a(3)            =    1 +   3        =    4 =  2^2
.  a(3) + a(4)            =    3 +   6        =    9 =  3^2
.  a(4) + a(5)            =    6 +   2        =    8 =  2^3
.  a(6)                                       =   16 =  2^4
.  a(5) + a(6) + a(7)     =    2 +  16 +   9  =   27 =  3^3
.  a(7) + a(8)            =    9 +  23        =   32 =  2^5
.  a(8) + a(9)            =   23 +  58        =   81 =  3^4
.  a(9) + a(10)           =   58 +   6        =   64 =  2^6
.  a(11)                                      =  128 =  2^7
.  a(10) + a(11) + a(12)  =    6 + 128 + 109  =  243 =  3^5
.  a(12) + a(13)          =  109 + 147        =  256 =  2^8
.  a(14)                                      =  512 =  2^9
.  a(13) + a(14) + a(15)  =  147 + 512 +  70  =  3^6 =  729 .

Prog

(Haskell)
a006895 n = a006895_list !! n
a006895_list = 1 : f 0 0 (tail a000079_list) (tail a000244_list) where
   f x y us'@(u:us) vs'@(v:vs)
     | x > 0     = (u - x) : f 0 (u - x + y) us vs'
     | y > v - u = (v - y) : f (v + x - y) 0 us' vs
     | otherwise =       u : f 0 (u + y) us vs'
-- Reinhard Zumkeller, Oct 09 2013

Crossrefs

Cf. A000079, A000244, A006899, A108906, A085239.

Sequence in context: A238973 A335444 A358646 * A202204 A289815 A125205

Adjacent sequences: A006892 A006893 A006894 * A006896 A006897 A006898

Keyword

nonn,nice

Author

N. J. A. Sloane, K. S. Brown [ kevin2003(AT)delphi.com ]

Status

approved