A305371 - OEIS

%I #17 Jun 02 2018 17:28:26

%S 1,2,0,4,1,8,0,6,1,16,0,10,1,20,0,32,1,12,0,18,1,36,0,24,1,34,0,28,1,

%T 64,0,14,1,48,0,66,1,40,0,22,1,72,0,38,1,80,0,42,1,68,0,26,1,96,0,30,

%U 1,128,0,44,1,82,0,132,1,50,0,76,1,130,0,52,1,74,0,144,1,46,0,192,1,54,0,136,1,70,0,56,1,134

%N The binary expansions of b(n+1) and b(n) are required to have 1's in common at exactly the positions where a(n) has a 1 in its binary expansion, where b() is A305369.

%C The definition here is a consequence (or restatement) of the definition of A305369. The connection with A109812 is at present only an empirical observation.

%H N. J. A. Sloane, <a href="/A305371/b305371.txt">Table of n, a(n) for n = 1..10000</a>

%H N. J. A. Sloane, <a href="/A305369/a305369.txt">Maple program</a>

%F Empirical: For k >= 0, a(4k+1)=1, a(4k+3)=0; for k >= 1, a(2k)=2*A109812(k).

%e a(8) = 6 = 110_2, which expresses the fact that A305369(8) = 6 = 110_2 and A303369(9) = 7 = 111_2 have binary expensions whose common 1's are 110_2.

%Y Cf. A305369, A109812.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 02 2018