A258033 - OEIS

%I #11 Feb 16 2016 10:04:49

%S 0,0,2,1,0,2,1,3,0,5,2,4,1,3,0,5,2,4,1,6,3,0,8,5,2,7,4,1,6,3,0,8,5,2,

%T 10,7,4,1,9,6,3,0,8,5,2,10,7,4,1,9,6,3,11,0,8,5,13,2,10,7,4,12,1,9,6,

%U 3,11,0,8,5,13,2,10,7,4,12,1,9,6,14,3

%N Fractal sequence derived from A022328.

%C The sequence is constructed as follows: after partitioning A022328 into segments starting with 0, in each segment the greatest term is to be deleted (see example and comment in A022328); length of k-th mentioned segment = A020914(k); respective greatest term = A056576(k);

%C this sequence is fractal, i.e. if the first occurrence of each n is removed, the resulting sequence is the original sequence;

%C A258051 is constructed from this sequence, applying the same transform as described above.

%H Reinhard Zumkeller, <a href="/A258033/b258033.txt">Table of n, a(n) for n = 1..10000</a>

%e Segments of A022328 starting with 0, deleted maxima in brackets:

%e .   1:  0 [1]

%e .   2:  0 2 1 [3]

%e .   3:  0 2 [4] 1 3

%e .   4:  0 5 2 4 1 [6] 3

%e .   5:  0 5 2 [7] 4 1 6 3

%e .   6:  0 8 5 2 7 4 1 [9] 6 3

%e .   7:  0 8 5 2 10 7 4 1 9 6 3 [11]

%e .   8:  0 8 5 2 10 7 4 [12] 1 9 6 3 11

%e .   9:  0 8 5 13 2 10 7 4 12 1 9 6 [14] 3 11

%e .  10:  0 8 5 13 2 10 7 [15] 4 12 1 9 6 14 3 11

%e .  11:  0 8 16 5 13 2 10 7 15 4 12 1 9 [17] 6 14 3 11

%e .  12:  0 8 16 5 13 2 10 18 7 15 4 12 1 9 17 6 14 3 11 [19]

%e .  13:  0 8 16 5 13 2 10 18 7 15 4 12 [20] 1 9 17 6 14 3 11 19

%e .  14:  0 8 16 5 13 21 2 10 18 7 15 4 12 20 1 9 17 6 14 [22] 3 11 19

%e .  15:  0 8 16 5 13 21 2 10 18 7 15 [23] 4 12 20 1 9 17 6 14 22 3 11 19

%o (Haskell)

%o import Data.List (delete)

%o a258033 n = a258033_list !! (n-1)

%o a258033_list = 0 : f (tail a022328_list) where

%o    f xs = (0 : (delete (maximum ys) ys)) ++ f zs

%o           where (ys, (_ : zs)) = span (> 0) xs

%Y Cf. A022328, A020914, A056576, A258051.

%K nonn

%O 1,3

%A _Clark Kimberling_ and _Reinhard Zumkeller_, May 16 2015