|
%I #13 Jan 01 2018 04:18:50
%S 2,5,7,10,14,18,21,23,26,29,31,34,37,39,42,46,50,53,55,58,62,66,69,71,
%T 74,78,82,85,87,90,93,95,98,101,103,106,110,114,117,119,122,125,127,
%U 130,133,135,138,142,146,149,151,154,157,159,162,165,167,170,174,178,181,183,186
%N Positions n such that A010060(n) + A010060(n+3) = 1.
%C Conjecture: In every sequence of numbers n such that A010060(n) + A010060(n+k) = 1, for fixed odd k, the odious (A000069) and evil (A001969) terms alternate. [From _Vladimir Shevelev_, Jul 31 2009]
%H G. C. Greubel, <a href="/A161580/b161580.txt">Table of n, a(n) for n = 1..10000</a>
%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. [_Vladimir Shevelev_, Jul 31 2009]
%F A001477 \ A161579.
%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 <= 200, n++, If[tm[n] + tm[n+3] == 1, Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Oct 24 2013 *)
%o (PARI) is(n)=hammingweight(n)%2+hammingweight(n+3)%2==1 \\ _Charles R Greathouse IV_, Mar 22 2013
%Y Cf. A131323 A036554, A010060, A121539, A079523, A081706, A161579
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Jun 14 2009
%E More terms from _R. J. Mathar_, Aug 17 2009
|
