A352200 a(0)=0, a(1)=1; thereafter, a(n) is the smallest number m not yet in the sequence such that the binary expansions of m and a(n-1) have a 1 in the same position, but the positions of the 1's in the binary expansions of m and a(n-2) are disjoint, except that the second condition is ignored if it would imply that no choice for m were possible.

0, 1, 3, 2, 6, 4, 5, 9, 8, 10, 7, 17, 16, 18, 11, 12, 20, 19, 33, 32, 34, 14, 13, 49, 48, 21, 15, 40, 96, 64, 65, 23, 22, 24, 41, 35, 66, 68, 28, 25, 67, 38, 36, 29, 26, 98, 37, 129, 128, 130, 27, 44, 100, 80, 144, 131, 39, 52, 88, 72, 30, 50, 97, 69, 132, 136, 42, 51, 81, 76, 46, 146, 145, 45, 70, 82, 56, 137, 71, 54, 152, 73, 99, 134, 140, 57

Offset: 0

Author

N. J. A. Sloane, Mar 26 2022

Keywords

• nonn
• base

Comments

The second condition is ignored precisely when the positions of the 1's in a(n-1) are a subset of the 1's in a(n-2).

This is a set-theory analog of A352187.

Examples

			a(0)=0 and a(1)=1=1_2 are given.
a(2) = 3 = 11_2 is disjoint from a(0) and intersects a(1).
a(3) = 2 = 10_2 is disjoint from a(1) and intersects a(2).
Now there is no choice for a(4) that meets both conditions, so we ignore the no-intersection-with-a(n-2) condition, and take a(4) = 6 = 110_2.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Maple program

Crossrefs

This completes a set of four pairs of sequences: (A064413 and A115510), (A098550 and A252867), (A336957 and A338833), (A352187 and this sequence, A352200).

Programs

Maple

See link.