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
KEYWORD
nonn
AUTHOR
Clark Kimberling and Reinhard Zumkeller, May 16 2015
STATUS
approved