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A106838 Numbers m such that m, m+1 and m+2 have odd part of the form 4*k+3.

%I A106838 #24 Sep 14 2024 06:50:27
%S A106838 22,46,54,86,94,110,118,150,174,182,190,214,222,238,246,278,302,310,
%T A106838 342,350,366,374,382,406,430,438,446,470,478,494,502,534,558,566,598,
%U A106838 606,622,630,662,686,694,702,726,734,750,758,766,790,814,822,854,862
%N A106838 Numbers m such that m, m+1 and m+2 have odd part of the form 4*k+3.
%C A106838 Either of form 2a(m)+2 or 32k+22, k>=0, 0<m<n.
%C A106838 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
%C A106838 The asymptotic density of this sequence is 1/16. - _Amiram Eldar_, Sep 14 2024
%H A106838 Vincenzo Librandi, <a href="/A106838/b106838.txt">Table of n, a(n) for n = 1..1000</a>
%H A106838 Bruce Bates, Martin Bunder, and Keith Tognetti, <a href="https://doi.org/10.2298/AADM1000005B">Mirroring and Interleaving in the Paperfolding Sequence</a>, Applicable Analysis and Discrete Mathematics, Volume 4, Number 1, April 2010, pages 96-118.
%F A106838 a(n) = 8*A091067(n) - 2.
%e A106838 22/2=11 is 3 mod 4 and so is 23 and 24/8=3, thus 22 is in sequence.
%t A106838 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 *)
%Y A106838 Cf. A091067, A106837, A106841.
%K A106838 nonn
%O A106838 1,1
%A A106838 _Ralf Stephan_, May 03 2005