A258033 Fractal sequence derived from A022328.

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

Offset: 1

Author

Clark Kimberling and Reinhard Zumkeller, May 16 2015

Keywords

• nonn

Comments

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);

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

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

Examples

			Segments of A022328 starting with 0, deleted maxima in brackets:
.   1:  0 [1]
.   2:  0 2 1 [3]
.   3:  0 2 [4] 1 3
.   4:  0 5 2 4 1 [6] 3
.   5:  0 5 2 [7] 4 1 6 3
.   6:  0 8 5 2 7 4 1 [9] 6 3
.   7:  0 8 5 2 10 7 4 1 9 6 3 [11]
.   8:  0 8 5 2 10 7 4 [12] 1 9 6 3 11
.   9:  0 8 5 13 2 10 7 4 12 1 9 6 [14] 3 11
.  10:  0 8 5 13 2 10 7 [15] 4 12 1 9 6 14 3 11
.  11:  0 8 16 5 13 2 10 7 15 4 12 1 9 [17] 6 14 3 11
.  12:  0 8 16 5 13 2 10 18 7 15 4 12 1 9 17 6 14 3 11 [19]
.  13:  0 8 16 5 13 2 10 18 7 15 4 12 [20] 1 9 17 6 14 3 11 19
.  14:  0 8 16 5 13 21 2 10 18 7 15 4 12 20 1 9 17 6 14 [22] 3 11 19
.  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
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A022328, A020914, A056576, A258051.

Programs

Haskell

import Data.List (delete)
a258033 n = a258033_list !! (n-1)
a258033_list = 0 : f (tail a022328_list) where
   f xs = (0 : (delete (maximum ys) ys)) ++ f zs
          where (ys, (_ : zs)) = span (> 0) xs