

A004741


Concatenation of sequences (1,3,..,2n1,2n,2n2,..,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 2k1 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. 221222.
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. AdamsWatters, Aug 28 2006


MATHEMATICA

Flatten[Table[{Range[1, 2n1, 2], Range[2n, 2, 2]}, {n, 10}]] (* Harvey P. Dale, Aug 12 2014 *)


PROG

(Haskell)
a004741 n = a004741_list !! (n1)
a004741_list = concat $ map (\n > [1, 3..2*n1] ++ [2*n, 2*n2..2]) [1..]
 Reinhard Zumkeller, Mar 26 2011


CROSSREFS

Sequence in context: A106382 A229287 A286539 * A133923 A341231 A334081
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



