OFFSET
0,5
COMMENTS
For example, for k = 3, take S_2 = {0,2,3,1} and insert 2^2 through 2^3-1 after the 0, so that S_3 = {0,4,5,6,7,2,3,1}. The string S_k has length 2^k.
A self-similar fractal sequence.
This is the sequence g_n at the end of Section 2 of Levine's paper. The paper also continues several other sequences that are probably not in the OEIS at present.
REFERENCES
L. Levine, Fractal sequences and restricted Nim, Ars Combin. 80 (2006), 113-127.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1022
L. Levine, Fractal sequences and restricted Nim, arXiv:math/0409408 [math.CO], 2004.
L. Levine, Home Page
FORMULA
If n=2^m-1, then a(n)=0; for all other terms, write n in binary, collapse the initial segment of 1's to a single 1 and delete the first 0. For example, a(25)=a(11001)=101=5. - Lionel Levine (levine(AT)Math.Berkeley.EDU), May 04 2006
a(n)=0 if n=2^m-1, otherwise A054429(2^ceiling(log_2(n+1))-n-1). - Peter Ward, Jan 23 2020
a(0)=0, a(1)=0; for all other terms, write n as 2^(m+1)+k with 0 <= k < 2^(m+1), then a(n)=2^m+k if k < 2^m, otherwise a(k). - Peter Ward, Jan 23 2020
EXAMPLE
The first few strings S_0, S_1, S_2, ... are as follows:
0
0,1
0,2,3,1
0,4,5,6,7,2,3,1
0,8,9,10,11,12,13,14,15,4,5,6,7,2,3,1
MATHEMATICA
Nest[Append[#, Join[{#[[-1, 1]]}, Range[#2, 2 #2 - 1], Rest@ #[[-1]]]] & @@ {#1, Length@ #[[-1]]} &, {{0}, {0, 1}}, 5] // Flatten (* Michael De Vlieger, Jan 25 2020 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Mar 10 2006
EXTENSIONS
Edited by Robert G. Wilson v, Apr 11 2006
Further edited by N. J. A. Sloane, Jan 16 2009
STATUS
approved