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

Author

R. Muller

Keywords

• nonn
• easy

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.

Programs

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

Mathematica

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

Formula

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

Extensions

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