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%I #25 May 18 2019 17:59:16
%S 1,3,4,5,7,10,14,17,19,20,21,23,25,27,28,29,31,33,35,36,37,39,42,46,
%T 49,51,52,53,55,58,62
%N Numbers such that A010060(n) = A010060(n+7).
%C Or union of intersection of A161673 and {A121539(n)-7} and intersection of A161639 and {A079523(n)-7}.
%C Conjecture: In every sequence of numbers n, such that A010060(n)=A010060(n+k), for fixed odd k, the odious (A000069) and evil (A001969) terms alternate. - _Vladimir Shevelev_, Jul 31 2009
%H Charles R Greathouse IV, <a href="/A162311/b162311.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 V. 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 <= 20000, n++, If[tm[n] == tm[n + 7], Sow[n]]]][[2, 1]] (* _G. C. Greubel_, Jan 05 2018 *)
%o (PARI) is(n)=hammingweight(n)%2==hammingweight(n+7)%2 \\ _Charles R Greathouse IV_, Aug 20 2013
%Y Cf. A161890, A161824, A161817, A161674, A161673, A161639, A161641, A161627, A161579, A161580, A121539, A131323, A036554, A010060, A079523, A081706, A161916, A161974.
%K nonn,base,easy
%O 1,2
%A _Vladimir Shevelev_, Jul 01 2009
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