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A004741 Concatenation of sequences (1,3,..,2n-1,2n,2n-2,..,2) for n >= 1. 2
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; text; internal format)
OFFSET

1,2

COMMENTS

Odd numbers increasing from 1 to 2k-1 followed by even numbers decreasing from 2k to 2.

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, see Kimberling link.

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].

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10100

C. Kimberling, Fractal sequences.

F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.

Eric Weisstein's World of Mathematics, Smarandache Sequences.

FORMULA

Ordinal transform of A004737. - Franklin T. Adams-Watters, Aug 28 2006

MATHEMATICA

Flatten[Table[{Range[1, 2n-1, 2], Range[2n, 2, -2]}, {n, 10}]] (* Harvey P. Dale, Aug 12 2014 *)

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

CROSSREFS

Sequence in context: A106382 A229287 A286539 * A133923 A125158 A273823

Adjacent sequences:  A004738 A004739 A004740 * A004742 A004743 A004744

KEYWORD

nonn,easy

AUTHOR

R. Muller

EXTENSIONS

Data corrected from 36th term on by  Reinhard Zumkeller, Mar 26 2011.

STATUS

approved

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Last modified April 19 18:37 EDT 2019. Contains 322290 sequences. (Running on oeis4.)