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

22, 46, 54, 86, 94, 110, 118, 150, 174, 182, 190, 214, 222, 238, 246, 278, 302, 310, 342, 350, 366, 374, 382, 406, 430, 438, 446, 470, 478, 494, 502, 534, 558, 566, 598, 606, 622, 630, 662, 686, 694, 702, 726, 734, 750, 758, 766, 790, 814, 822, 854, 862

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Bruce Bates, Martin Bunder, 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

Cf. A091067, A106837, A106841.

Sequence in context: A041964 A041966 A350321 * A190614 A281187 A335297

Adjacent sequences: A106835 A106836 A106837 * A106839 A106840 A106841

Keyword

nonn

Author

Ralf Stephan, May 03 2005

Status

approved