A004741 Concatenation of sequences (1,3,..,2n-1,2n,2n-2,..,2) for n >= 1.

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

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

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

J. Brown et al., Problem 4619, School Science and Mathematics (USA), Vol. 97(4), 1997, pp. 221-222.

Clark 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 * A352840 A133923 A347296

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