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A007606
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Take 1, skip 2, take 3, etc.
(Formerly M3241)
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8
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1, 4, 5, 6, 11, 12, 13, 14, 15, 22, 23, 24, 25, 26, 27, 28, 37, 38, 39, 40, 41, 42, 43, 44, 45, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 137, 138
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| List the natural numbers: 1, 2, 3, 4, 5, 6, 7, ... . Keep the first number (1), delete the next two numbers (2, 3), keep the next three numbers (4, 5, 6), delete the next four numbers (7, 8, 9, 10) and so on.
Sometimes called the Smarandache sequential sieve.
a(A000290(n)) = A000384(n). [Reinhard Zumkeller, Feb 12 2011]
A057211(a(n)) = 1. [Reinhard Zumkeller, Dec 30 2011]
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REFERENCES
| C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I, Erhus Publ., Glendale, 1994.
R. Honsberger, Mathematical Gems III, M.A.A., 1985, p. 177.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
F. Smarandache, Properties of Numbers, 1972.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 13 2009]
C. Dumitrescu & V. Seleacu, editors, Some Notions and Questions in Number Theory, Vol. I.
Index entries for sequences generated by sieves
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FORMULA
| a(n) = n + m*(m+1) where m = floor(sqrt(n-1)). - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Mar 26 2004
a(n+1) = a(n) + if n=k^2 then 2*k+1 else 1; a(1) = 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 13 2009]
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MATHEMATICA
| Flatten[ Table[i, {j, 1, 17, 2}, {i, j(j - 1)/2 + 1, j(j + 1)/2}]] (from Robert G. Wilson v Mar 11 2004)
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PROG
| (PARI) for(n=1, 66, m=sqrtint(n-1); print1(n+m*(m+1), ", "))
(Haskell)
a007606 n = a007606_list !! (n-1)
a007606_list = takeSkip 1 [1..] where
takeSkip k xs = take k xs ++ takeSkip (k + 2) (drop (2*k + 1) xs)
-- Reinhard Zumkeller, Feb 12 2011
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CROSSREFS
| Complement of A007607.
Cf. A007950, A007951, A007952, A048859, A004201.
Sequence in context: A101590 A057916 A162415 * A047311 A076138 A050037
Adjacent sequences: A007603 A007604 A007605 * A007607 A007608 A007609
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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