A258051 Fractal sequence derived from A258033.

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, 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, 7, 4, 12, 1, 9, 6, 3, 11, 0, 8, 5, 13, 2, 10, 7, 15, 4

Offset

1,5

Comments

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);

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

Links

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

Example

Segments of A258033 starting with 0, deleted maxima in brackets:
.   1:  0
.   2:  0 [2] 1
.   3:  0 2 1 [3]
.   4:  0 [5] 2 4 1 3
.   5:  0 5 2 4 1 [6] 3
.   6:  0 [8] 5 2 7 4 1 6 3
.   7:  0 8 5 2 [10] 7 4 1 9 6 3
.   8:  0 8 5 2 10 7 4 1 9 6 3 [11]
.   9:  0 8 5 [13] 2 10 7 4 12 1 9 6 3 11
.  10:  0 8 5 13 2 10 7 4 12 1 9 6 [14] 3 11
.  11:  0 8 [16] 5 13 2 10 7 15 4 12 1 9 6 14 3 11
.  12:  0 8 16 5 13 2 10 [18] 7 15 4 12 1 9 17 6 14 3 11
.  13:  0 8 16 5 13 2 10 18 7 15 4 12 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 3 11 19
.  15:  0 8 16 5 13 21 2 10 18 7 15 4 12 20 1 9 17 6 14 [22] 3 11 19

Prog

(Haskell)
import Data.List (delete)
a258051 n = a258051_list !! (n-1)
a258051_list = f (tail a258033_list) where
   f xs = (0 : (delete (maximum ys) ys)) ++ f zs
          where (ys, (_ : zs)) = span (> 0) xs

Crossrefs

%Cf. A258033, A022328.

Sequence in context: A141343 A256678 A066709 * A174026 A226075 A279226

Adjacent sequences: A258048 A258049 A258050 * A258052 A258053 A258054

Keyword

nonn

Author

Clark Kimberling and Reinhard Zumkeller, May 17 2015

Status

approved