A352200 - OEIS

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.

%I #22 Mar 27 2022 05:57:33

%S 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,

%T 15,40,96,64,65,23,22,24,41,35,66,68,28,25,67,38,36,29,26,98,37,129,

%U 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

%N 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.

%C 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).

%C This is a set-theory analog of A352187.

%H N. J. A. Sloane, <a href="/A352200/b352200.txt">Table of n, a(n) for n = 0..10000</a>

%H N. J. A. Sloane, <a href="/A352200/a352200.txt">Maple program</a>

%e a(0)=0 and a(1)=1=1_2 are given.

%e a(2) = 3 = 11_2 is disjoint from a(0) and intersects a(1).

%e a(3) = 2 = 10_2 is disjoint from a(1) and intersects a(2).

%e 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.

%p See link.

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

%K nonn,base

%O 0,3

%A _N. J. A. Sloane_, Mar 26 2022