



0, 1, 2, 3, 6, 7, 8, 9, 12, 13, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 44, 45, 48, 49, 50, 51, 54, 55, 56, 57, 60, 61, 64, 65, 66, 67, 70, 71, 72, 73, 76, 77, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 94, 95, 96, 97, 98, 99, 102, 103, 104, 105, 108
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OFFSET

0,3


COMMENTS

Let A=Axxxxxx be any sequence from OEIS. Denote by A^* the intersection of the union of sequences {2*A(n)+j}, j=0,1, and the union of sequences {4*A(n)+k}, k=2,1,0,1. Then the sequence is the union of (A079523)^* and (A121539)^*.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000
J.P. Allouche, Thue, Combinatorics on words, and conjectures inspired by the ThueMorse sequence, arXiv:1401.3727 [math.NT], 2014.
J.P. Allouche, Thue, Combinatorics on words, and conjectures inspired by the ThueMorse sequence, J. de ThÃ©orie des Nombres de Bordeaux, 27, no. 2 (2015), 375388.
V. Shevelev, Equations of the form t(x+a)=t(x) and t(x+a)=1t(x) for ThueMorse sequence, arXiv:0907.0880 [math.NT], 20092012.


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 <= 6000, n++, If[tm[n] == tm[n + 6], Sow[n]]]][[2, 1]] (* G. C. Greubel, Jan 05 2018 *)


PROG

(PARI) is(n)=hammingweight(n)%2==hammingweight(n+6)%2 \\ Charles R Greathouse IV, Aug 20 2013


CROSSREFS

Cf. A161817, A161674, A161673, A161639, A161641, A161627, A161579, A161580, A121539, A131323, A036554, A010060, A079523, A081706.
Sequence in context: A039029 A037460 A285134 * A102806 A275884 A003605
Adjacent sequences: A161821 A161822 A161823 * A161825 A161826 A161827


KEYWORD

nonn,base


AUTHOR

Vladimir Shevelev, Jun 20 2009


EXTENSIONS

Terms a(40) onwards added by G. C. Greubel, Jan 05 2018


STATUS

approved



