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Search: id:A005243
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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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+0
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; listen)
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OFFSET
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1,2
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COMMENT
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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 (reinhard.zumkeller(AT)gmail.com), Apr 13 2006
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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EXAMPLE
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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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CROSSREFS
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Complement of A048973.
Cf. A118065, A118166.
Sequence in context: A092979 A135260 A085921 this_sequence A117045 A025055 A080276
Adjacent sequences: A005240 A005241 A005242 this_sequence A005244 A005245 A005246
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KEYWORD
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nonn,nice,easy
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AUTHOR
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D. R. Hofstadter
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net)
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