A258051 - OEIS

%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