A161580 Positions n such that A010060(n) + A010060(n+3) = 1.

2, 5, 7, 10, 14, 18, 21, 23, 26, 29, 31, 34, 37, 39, 42, 46, 50, 53, 55, 58, 62, 66, 69, 71, 74, 78, 82, 85, 87, 90, 93, 95, 98, 101, 103, 106, 110, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 142, 146, 149, 151, 154, 157, 159, 162, 165, 167, 170, 174, 178, 181, 183, 186

Offset: 1

Author

Vladimir Shevelev, Jun 14 2009

Keywords

• nonn

Comments

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]

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• 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. [_Vladimir Shevelev_, Jul 31 2009]

Crossrefs

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

Programs

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+3] == 1, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 24 2013 *)

PARI

is(n)=hammingweight(n)%2+hammingweight(n+3)%2==1 \\ Charles R Greathouse IV, Mar 22 2013

Formula

A001477 \ A161579.

Extensions

More terms from R. J. Mathar, Aug 17 2009