This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004741 #39 Feb 16 2025 08:32:28
%S A004741 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 A004741 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 A004741 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 A004741 Concatenation of sequences (1,3,..,2n-1,2n,2n-2,..,2) for n >= 1.
%C A004741 Odd numbers increasing from 1 to 2k-1 followed by even numbers decreasing from 2k to 2.
%C A004741 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 A004741 This is a fractal sequence, see Kimberling link.
%D A004741 F. Smarandache, "Numerical Sequences", University of Craiova, 1975; [Arizona State University, Special Collection, Tempe, AZ, USA].
%H A004741 Vincenzo Librandi, <a href="/A004741/b004741.txt">Table of n, a(n) for n = 1..10100</a>
%H A004741 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 A004741 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/fractals.html">Fractal sequences</a>.
%H A004741 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">Sequences of Numbers Involved in Unsolved Problems</a>.
%H A004741 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>.
%F A004741 Ordinal transform of A004737. - _Franklin T. Adams-Watters_, Aug 28 2006
%t A004741 Flatten[Table[{Range[1,2n-1,2],Range[2n,2,-2]},{n,10}]] (* _Harvey P. Dale_, Aug 12 2014 *)
%o A004741 (Haskell)
%o A004741 a004741 n = a004741_list !! (n-1)
%o A004741 a004741_list = concat $ map (\n -> [1,3..2*n-1] ++ [2*n,2*n-2..2]) [1..]
%o A004741 -- _Reinhard Zumkeller_, Mar 26 2011
%K A004741 nonn,easy
%O A004741 1,2
%A A004741 R. Muller
%E A004741 Data corrected from 36th term on by _Reinhard Zumkeller_, Mar 26 2011