A161627 Positions n such that A010060(n)=A010060(n+4).

4, 5, 6, 7, 20, 21, 22, 23, 28, 29, 30, 31, 36, 37, 38, 39, 52, 53, 54, 55, 68, 69, 70, 71, 84, 85, 86, 87, 92, 93, 94, 95, 100, 101, 102, 103, 116, 117, 118, 119, 124, 125, 126, 127, 132, 133, 134, 135, 148, 149, 150, 151, 156, 157, 158, 159, 164, 165, 166, 167, 180, 181, 182

Offset

1,1

Comments

Or: union of the numbers of the form 4*A079523(n)+k, k=0, 1, 2, or 3.

Locates patterns of the form 1xxx1 or 0xxx0 in the Thue-Morse sequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

J.-P. Allouche, Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence, arXiv preprint arXiv:1401.3727 [math.NT], 2014.

J.-P. Allouche, Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence, J. de Théorie des Nombres de Bordeaux, 27, no. 2 (2015), 375-388.

V. Shevelev, Equations of the form t(x+a)=t(x) and t(x+a)=1-t(x) for Thue-Morse sequence arXiv:0907.0880 [math.NT], 2009-2012. [From Vladimir Shevelev, Jul 31 2009]

Mathematica

tm[0] = 0; tm[n_?EvenQ] := tm[n] = tm[n/2]; tm[n_] := tm[n] = 1 - tm[(n-1)/2]; Reap[For[n = 0, n <= 200, n++, If[tm[n] == tm[n+4], Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 24 2013 *)
SequencePosition[ThueMorse[Range[200]], {x_, _, _, _, x_}][[All, 1]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Apr 16 2017 *)

Prog

(PARI) is(n)=hammingweight(n)%2==hammingweight(n+4)%2 \\ Charles R Greathouse IV, Aug 20 2013

Crossrefs

Cf. A161579, A161580, A079523, A131323, A036554, A010060, A121539, A079523, A081706.

Sequence in context: A233035 A250036 A107759 * A030667 A030677 A071177

Adjacent sequences: A161624 A161625 A161626 * A161628 A161629 A161630

Keyword

nonn

Author

Vladimir Shevelev, Jun 15 2009

Extensions

Extended by R. J. Mathar, Aug 28 2009

Status

approved