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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), ....
(Formerly M0158)
3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A238973 A335444 A358646 * A202204 A289815 A125205
KEYWORD
nonn,nice
AUTHOR
N. J. A. Sloane, K. S. Brown [ kevin2003(AT)delphi.com ]
STATUS
approved

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Last modified May 20 05:07 EDT 2024. Contains 372703 sequences. (Running on oeis4.)