A305371 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.

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, 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, 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

Offset: 1

Author

N. J. A. Sloane, Jun 02 2018

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• N. J. A. Sloane, Maple program

Crossrefs

Cf. A305369, A109812.

Formula

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