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Positions n such that A010060(n) + A010060(n+8) = 1.
8

%I #10 Jan 06 2018 10:57:54

%S 0,1,2,3,4,5,6,7,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,

%T 33,34,35,36,37,38,39,48,49,50,51,52,53,54,55,64,65,66,67,68,69,70,71,

%U 80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103

%N Positions n such that A010060(n) + A010060(n+8) = 1.

%C Also union of numbers of the form 8*A121539(n)+k, 0<=k<8.

%C Generalization: the numbers n such that A010060(n)+A010060(n+2^m)=1 constitute the union of sequences {2^m*A121539(n)+k}, k=0,1,...,2^m-1.

%H G. C. Greubel, <a href="/A161673/b161673.txt">Table of n, a(n) for n = 1..10000</a>

%F A001477 \ A161639.

%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 + 8] == 1, Sow[n]]]][[2, 1]] (* _G. C. Greubel_, Jan 05 2018 *)

%o (PARI) is(n)=hammingweight(n)%2!=hammingweight(n+8)%2 \\ _Charles R Greathouse IV_, Aug 20 2013

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

%K nonn

%O 1,3

%A _Vladimir Shevelev_, Jun 16 2009

%E Edited and extended by _R. J. Mathar_, Sep 02 2009