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nonn,new,base

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

Under construction do not touch

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

See link.

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a(0)=0, a(1)=1, a(2)=3; 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.

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

a(0)=0, and a(1)=1=1_2, a(2)=3=11_2 are given.

a(3) = 2 ) = 3 = 10_11_2 is disjoint from a(10) and intersects a(1).

a(3) = 2 = 10_2 is the smallest possible value disjoint from a(1) and does not lead to intersects a contradiction(2).

a(2)=3=11_2 Now there is the smallest value no choice for a(4) that satisfies the meets both conditions. It does not lead to , so we ignore the no-intersection-with-a(n-2) condition, and take a contradiction(4) = 6 = 110_2.

a(3)=2=10_2 is the smallest value that satisfies the conditions, but then there is no choice for a(4). a(3)=6=110_2 is the next possibility, and does not lead to a contradiction.

a(4)=100_2 is the smallest value that satisfies the conditions, but then there is no choice for a(5). But a(4)=12=1100_2 works, and does not lead to a contradiction.

a(0)=0, a(1)=1=1_2, a(2)=3=11_2 are given.

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

is the smallest possible value and does not lead to a contradiction.

a(2)=3=11_2 is the smallest value that satisfies the conditions. It does not lead to a contradiction.

a(3)=2=10_2 is the smallest value that satisfies the conditions, but then there is no choice for a(4). a(3)=6=110_2 is the next possibility, and does not lead to a contradiction.

a(4)=100_2 is the smallest value that satisfies the conditions, but then there is no choice for a(5). But a(4)=12=1100_2 works, and does not lead to a contradiction.

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