A258033 -id:A258033 - cp's OEIS frontend

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

Clark Kimberling and Reinhard Zumkeller, May 17 2015

nonn

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.

			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

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

%Cf. A258033, A022328.

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

cp's OEIS Frontend

A258051 Fractal sequence derived from A258033.

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Haskell