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A005243
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A self-generating sequence: start with 1 and 2, take all sums of any number of successive previous elements and adjoin them to the sequence. Repeat!
(Formerly M0623)
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9
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1, 2, 3, 5, 6, 8, 10, 11, 14, 16, 17, 18, 19, 21, 22, 24, 25, 29, 30, 32, 33, 34, 35, 37, 40, 41, 43, 45, 46, 47, 49, 51, 54, 57, 58, 59, 60, 62, 65, 67, 68, 69, 70, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Most of the natural numbers are members. Conjecture: there are infinitely many nonmembers. Is there an estimate for a(k)/k ?
A118164(n) = number of representations of a(n) as sum of consecutive earlier terms. - Reinhard Zumkeller, Apr 13 2006
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REFERENCES
| R. K. Guy, Unsolved Problems in Number Theory, E31.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Hofstadter Sequences.
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EXAMPLE
| After 1,2,3,5,6 you can adjoin 8 = 3+5, 10 = 2+3+5, etc.
12 is not a term since it is not the sum of any set of consecutive previous terms.
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MATHEMATICA
| f[s_] := (ls = Length[s]; ft = Flatten[Table[Take[s, {j, k}], {j, 1, ls-1}, {k, j+1, ls}], 1]; Union[s, Apply[Plus, ft, {1}]]); Take[Nest[f, {1, 2, 3}, 5], 67]
(* From Jean-François Alcover, Jul 27 2011 *)
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PROG
| (Haskell)
a005243 n = a005243_list !! (n-1)
a005243_list = 1 : h [1] (singleton 2) where
h xs s =
m : h (m:xs) (foldl (flip insert) s'
(map (+ m) (map sum $ tail $ inits xs))) where
(m, s') = deleteFindMin s
-- Reinhard Zumkeller, Jun 22 06 2011
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CROSSREFS
| Complement of A048973.
Cf. A118065, A118166.
Sequence in context: A135260 A179180 A085921 * A117045 A025055 A080276
Adjacent sequences: A005240 A005241 A005242 * A005244 A005245 A005246
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KEYWORD
| nonn,nice,easy
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AUTHOR
| D. R. Hofstadter
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EXTENSIONS
| More terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu)
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