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