cp's OEIS Frontend

A258033 Fractal sequence derived from A022328.

%I A258033 #11 Feb 16 2016 10:04:49
%S A258033 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 A258033 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 A258033 3,11,0,8,5,13,2,10,7,4,12,1,9,6,14,3
%N A258033 Fractal sequence derived from A022328.
%C A258033 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 A258033 this sequence is fractal, i.e. if the first occurrence of each n is removed, the resulting sequence is the original sequence;
%C A258033 A258051 is constructed from this sequence, applying the same transform as described above.
%H A258033 Reinhard Zumkeller, <a href="/A258033/b258033.txt">Table of n, a(n) for n = 1..10000</a>
%e A258033 Segments of A022328 starting with 0, deleted maxima in brackets:
%e A258033 .   1:  0 [1]
%e A258033 .   2:  0 2 1 [3]
%e A258033 .   3:  0 2 [4] 1 3
%e A258033 .   4:  0 5 2 4 1 [6] 3
%e A258033 .   5:  0 5 2 [7] 4 1 6 3
%e A258033 .   6:  0 8 5 2 7 4 1 [9] 6 3
%e A258033 .   7:  0 8 5 2 10 7 4 1 9 6 3 [11]
%e A258033 .   8:  0 8 5 2 10 7 4 [12] 1 9 6 3 11
%e A258033 .   9:  0 8 5 13 2 10 7 4 12 1 9 6 [14] 3 11
%e A258033 .  10:  0 8 5 13 2 10 7 [15] 4 12 1 9 6 14 3 11
%e A258033 .  11:  0 8 16 5 13 2 10 7 15 4 12 1 9 [17] 6 14 3 11
%e A258033 .  12:  0 8 16 5 13 2 10 18 7 15 4 12 1 9 17 6 14 3 11 [19]
%e A258033 .  13:  0 8 16 5 13 2 10 18 7 15 4 12 [20] 1 9 17 6 14 3 11 19
%e A258033 .  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 A258033 .  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 A258033 (Haskell)
%o A258033 import Data.List (delete)
%o A258033 a258033 n = a258033_list !! (n-1)
%o A258033 a258033_list = 0 : f (tail a022328_list) where
%o A258033    f xs = (0 : (delete (maximum ys) ys)) ++ f zs
%o A258033           where (ys, (_ : zs)) = span (> 0) xs
%Y A258033 Cf. A022328, A020914, A056576, A258051.
%K A258033 nonn
%O A258033 1,3
%A A258033 _Clark Kimberling_ and _Reinhard Zumkeller_, May 16 2015