OFFSET
1,1
COMMENTS
Either of form 2a(m)+2 or 32k+22, k>=0, 0<m<n.
Number points of the Heighway/Harter dragon curve starting m=0 at the origin. Those m with odd part 4k+3 (A091067) are where the curve turns right. So this sequence is the first m of each run of 3 consecutive right turns. There are no runs of 4 or more since the turn at odd m alternates left and right. Bates, Bunder, and Tognetti (Theorem 19, page 104), show the last of each run is integers of the form 2^p*(4k+3) with p>=3. So here the first of each run is a(n) = 8*A091067(n)-2 as Ralf Stephan already noted. - Kevin Ryde, Mar 12 2020
The asymptotic density of this sequence is 1/16. - Amiram Eldar, Sep 14 2024
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Bruce Bates, Martin Bunder, and Keith Tognetti, Mirroring and Interleaving in the Paperfolding Sequence, Applicable Analysis and Discrete Mathematics, Volume 4, Number 1, April 2010, pages 96-118.
FORMULA
a(n) = 8*A091067(n) - 2.
EXAMPLE
22/2=11 is 3 mod 4 and so is 23 and 24/8=3, thus 22 is in sequence.
MATHEMATICA
opm4[n_]:=Mod[n/2^IntegerExponent[n, 2], 4]; Flatten[Position[Partition[ Table[opm4[n], {n, 1000}], 3, 1], {3, 3, 3}]] (* Harvey P. Dale, Feb 01 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ralf Stephan, May 03 2005
STATUS
approved