OFFSET
1,3
COMMENTS
This is a fractal sequence.
It appears that each group of 2^k terms starts with 1 and ends with the remaining powers of two from 2^k down to 2^1.
From Antti Karttunen, Jan 09-12 2016: (Start)
This is ordinal transform of A265332, which is modified A051135 (with a(1) = 1, instead of 2). - after Franklin T. Adams-Watters' original definition for this sequence.
A000079 (powers of 2) indeed gives the positions of ones in this sequence. This follows from the properties (3) and (4) of A004001 given on page 227 of Kubo & Vakil paper (page 3 of PDF), which together also imply the pattern observed above, more clearly represented as:
a(2) = 1.
a(3..4) = 2, 1.
a(6..8) = 4, 2, 1.
a(13..16) = 8, 4, 2, 1.
a(28..31) = 16, 8, 4, 2, 1.
etc.
(End)
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..8192
T. Kubo and R. Vakil, On Conway's recursive sequence, Discr. Math. 152 (1996), 225-252.
FORMULA
MATHEMATICA
PROG
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Franklin T. Adams-Watters, Jul 07 2009
EXTENSIONS
Name amended by Antti Karttunen, Jan 09 2016
STATUS
approved