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A004741
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Concatenation of sequences (1,3,..,2n-1,2n,2n-2,..,2) for n >= 1.
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1, 2, 1, 3, 4, 2, 1, 3, 5, 6, 4, 2, 1, 3, 5, 7, 8, 6, 4, 2, 1, 3, 5, 7, 9, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Odd numbers increasing from 1 to 2k-1 followed by even numbers decreasing from 2k to 2.
Also called Smarandache Permutation Sequence.
The ordinal transform of a sequence b_0, b_1, b_2, ... is the sequence a_0, a_1, a_2, ... where a_n is the number of times b_n has occurred in {b_0 ... b_n}.
This is a fractal sequence.
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REFERENCES
| J. Brown et al., Problem 4619, School Science and Mathematics (USA), Vol. 97(4), 1997, pp. 221-222.
F. Smarandache, "Numerical Sequences", University of Craiova, 1975; [Arizona State University, Special Collection, Tempe, AZ, USA].
F. Smarandache, "Collected Papers", Vol. II, Tempus Publ. Hse., Bucharest, 1996.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
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LINKS
| M. L. Perez et al., eds., Smarandache Notions Journal
C. Kimberling, Fractal sequences
F. Smarandache, Collected Papers, Vol. II
Eric Weisstein's World of Mathematics, Smarandache Sequences.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
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FORMULA
| Ordinal transform of A004737. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 28 2006
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PROG
| (Haskell)
a004741 n = a004741_list !! (n-1)
a004741_list = concat $ map (\n -> [1, 3..2*n-1] ++ [2*n, 2*n-2..2]) [1..]
-- Reinhard Zumkeller, Mar 26 2011
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CROSSREFS
| Sequence in context: A154929 A049400 A106382 * A133923 A125158 A112384
Adjacent sequences: A004738 A004739 A004740 * A004742 A004743 A004744
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KEYWORD
| nonn,easy
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AUTHOR
| R. Muller
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EXTENSIONS
| Data corrected from 36th term on by Reinhard Zumkeller, Mar 26 2011.
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