A227928 Powers of 2 or of 3 in order as occurring in the two ways of parenthesizing the terms in A006895.

1, 2, 3, 4, 9, 8, 16, 27, 32, 81, 64, 128, 243, 256, 512, 729, 1024, 2187, 2048, 4096, 6561, 8192, 19683, 16384, 32768, 59049, 65536, 131072, 177147, 262144, 531441, 524288, 1048576, 1594323, 2097152, 4782969, 4194304, 8388608, 14348907, 16777216, 43046721

Offset: 1

Author

Reinhard Zumkeller, Oct 09 2013

Keywords

• nonn

Comments

Permutation of A006899, a(n) = A006899(n+k) for some k in {-1,0,1}.

Examples

			.  n  |  a(n)                       let x denote A006895
. ----+------
.   1 |    1                     =  x(0)
.   2 |    2                     =  x(1)
.   3 |    3  =   2 +   1        =  x(1) + x(2)
.   4 |    4  =   1 +   3        =  x(2) + x(3)
.   5 |    9  =   3 +   6        =  x(3) + x(4)
.   6 |    8  =   6 +   2        =  x(4) + x(5)
.   7 |   16                     =  x(6)
.   8 |   27  =   2 +  16 +   9  =  x(5) + x(6) + x(7)
.   9 |   32  =   9 +  23        =  x(7) + x(8)
.  10 |   81  =  23 +  58        =  x(8) + x(9)
.  11 |   64  =  58 +   6        =  x(9) + x(10)
.  12 |  128                     =  x(11)
.  13 |  243  =   6 + 128 + 109  =  x(10) + x(11) + x(12)
.  14 |  256  = 109 + 147        =  x(12) + x(13)
.  15 |  512                     =  x(14)
.  16 |  729  = 147 + 512 +  70  =  x(13) + x(14) + x(15) .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Programs

Haskell

a227928 n = a227928_list !! (n-1)
a227928_list = 1 : f 0 0 (tail a000079_list) (tail a000244_list) where
   f x y us'@(u:us) vs'@(v:vs)
     | x > 0     = u : f 0 (u - x + y) us vs'
     | y > v - u = v : f (v + x - y) 0 us' vs
     | otherwise = u : f 0 (u + y) us vs'