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

1,2

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.

Links

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

N. J. A. Sloane, Maple program

Formula

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

Example

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.

Crossrefs

Cf. A305369, A109812.

Sequence in context: A168036 A371499 A217930 * A355018 A177256 A199891

Adjacent sequences: A305368 A305369 A305370 * A305372 A305373 A305374

Keyword

nonn

Author

N. J. A. Sloane, Jun 02 2018

Status

approved