A161824 - OEIS

%I #38 Apr 16 2023 21:44:40

%S 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,

%T 35,38,39,40,41,44,45,48,49,50,51,54,55,56,57,60,61,64,65,66,67,70,71,

%U 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

%N Numbers such that A010060(n) = A010060(n+6).

%C 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)^*.

%H G. C. Greubel, <a href="/A161824/b161824.txt">Table of n, a(n) for n = 1..10000</a>

%H J.-P. Allouche, <a href="http://arxiv.org/abs/1401.3727">Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence</a>, arXiv:1401.3727 [math.NT], 2014.

%H J.-P. Allouche, <a href="http://dx.doi.org/10.5802/jtnb.906">Thue, Combinatorics on words, and conjectures inspired by the Thue-Morse sequence</a>, J. de Théorie des Nombres de Bordeaux, 27, no. 2 (2015), 375-388.

%H Vladimir Shevelev, <a href="http://arXiv.org/abs/0907.0880">Equations of the form t(x+a)=t(x) and t(x+a)=1-t(x) for Thue-Morse sequence</a>, arXiv:0907.0880 [math.NT], 2009-2012.

%t 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 *)

%o (PARI) is(n)=hammingweight(n)%2==hammingweight(n+6)%2 \\ _Charles R Greathouse IV_, Aug 20 2013

%Y Cf. A161817, A161674, A161673, A161639, A161641, A161627, A161579, A161580, A121539, A131323, A036554, A010060, A079523, A081706.

%K nonn,base

%O 1,3

%A _Vladimir Shevelev_, Jun 20 2009

%E Terms a(40) onwards added by _G. C. Greubel_, Jan 05 2018

%E Offset corrected by _Mohammed Yaseen_, Mar 29 2023