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A258051 Fractal sequence derived from A258033.

%I A258051 #5 Feb 15 2016 12:19:51
%S A258051 0,0,1,0,2,1,0,2,4,1,3,0,5,2,4,1,3,0,5,2,7,4,1,6,3,0,8,5,2,7,4,1,9,6,
%T A258051 3,0,8,5,2,10,7,4,1,9,6,3,0,8,5,2,10,7,4,12,1,9,6,3,11,0,8,5,13,2,10,
%U A258051 7,4,12,1,9,6,3,11,0,8,5,13,2,10,7,15,4
%N A258051 Fractal sequence derived from A258033.
%C A258051 The sequence is constructed like A258033 is constructed: after partitioning A258033 into segments starting with 0, in each segment the greatest term is to be deleted (see example);
%C A258051 this sequence is fractal, i.e. if the first occurrence of each n is removed, the resulting sequence is the original sequence.
%H A258051 Reinhard Zumkeller, <a href="/A258051/b258051.txt">Table of n, a(n) for n = 1..10000</a>
%e A258051 Segments of A258033 starting with 0, deleted maxima in brackets:
%e A258051 .   1:  0
%e A258051 .   2:  0 [2] 1
%e A258051 .   3:  0 2 1 [3]
%e A258051 .   4:  0 [5] 2 4 1 3
%e A258051 .   5:  0 5 2 4 1 [6] 3
%e A258051 .   6:  0 [8] 5 2 7 4 1 6 3
%e A258051 .   7:  0 8 5 2 [10] 7 4 1 9 6 3
%e A258051 .   8:  0 8 5 2 10 7 4 1 9 6 3 [11]
%e A258051 .   9:  0 8 5 [13] 2 10 7 4 12 1 9 6 3 11
%e A258051 .  10:  0 8 5 13 2 10 7 4 12 1 9 6 [14] 3 11
%e A258051 .  11:  0 8 [16] 5 13 2 10 7 15 4 12 1 9 6 14 3 11
%e A258051 .  12:  0 8 16 5 13 2 10 [18] 7 15 4 12 1 9 17 6 14 3 11
%e A258051 .  13:  0 8 16 5 13 2 10 18 7 15 4 12 1 9 17 6 14 3 11 [19]
%e A258051 .  14:  0 8 16 5 13 [21] 2 10 18 7 15 4 12 20 1 9 17 6 14 3 11 19
%e A258051 .  15:  0 8 16 5 13 21 2 10 18 7 15 4 12 20 1 9 17 6 14 [22] 3 11 19
%o A258051 (Haskell)
%o A258051 import Data.List (delete)
%o A258051 a258051 n = a258051_list !! (n-1)
%o A258051 a258051_list = f (tail a258033_list) where
%o A258051    f xs = (0 : (delete (maximum ys) ys)) ++ f zs
%o A258051           where (ys, (_ : zs)) = span (> 0) xs
%Y A258051 %Cf. A258033, A022328.
%K A258051 nonn
%O A258051 1,5
%A A258051 _Clark Kimberling_ and _Reinhard Zumkeller_, May 17 2015