A004741 - OEIS

%I #38 Feb 05 2021 12:04:25

%S 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,

%T 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,

%U 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

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

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

%C 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}.

%C This is a fractal sequence, see Kimberling link.

%D F. Smarandache, "Numerical Sequences", University of Craiova, 1975; [Arizona State University, Special Collection, Tempe, AZ, USA].

%H Vincenzo Librandi, <a href="/A004741/b004741.txt">Table of n, a(n) for n = 1..10100</a>

%H J. Brown et al., <a href="https://doi.org/10.1111/j.1949-8594.1997.tb17373.x">Problem 4619</a>, School Science and Mathematics (USA), Vol. 97(4), 1997, pp. 221-222.

%H Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">Fractal sequences</a>.

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">Sequences of Numbers Involved in Unsolved Problems</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>.

%F Ordinal transform of A004737. - _Franklin T. Adams-Watters_, Aug 28 2006

%t Flatten[Table[{Range[1,2n-1,2],Range[2n,2,-2]},{n,10}]] (* _Harvey P. Dale_, Aug 12 2014 *)

%o (Haskell)

%o a004741 n = a004741_list !! (n-1)

%o a004741_list = concat $ map (\n -> [1,3..2*n-1] ++ [2*n,2*n-2..2]) [1..]

%o -- _Reinhard Zumkeller_, Mar 26 2011

%K nonn,easy

%O 1,2

%A R. Muller

%E Data corrected from 36th term on by _Reinhard Zumkeller_, Mar 26 2011