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A258033 Fractal sequence derived from A022328. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

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

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A022328, A020914, A056576, A258051.

Sequence in context: A022329 A087466 A333211 * A153248 A221179 A153247

Adjacent sequences:  A258030 A258031 A258032 * A258034 A258035 A258036

KEYWORD

nonn

AUTHOR

Clark Kimberling and Reinhard Zumkeller, May 16 2015

STATUS

approved

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Last modified September 30 02:03 EDT 2020. Contains 337432 sequences. (Running on oeis4.)