A351691 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>2, a(n) has a common factor with a(n-1), shares a 1-bit in its binary expansion with a(n-1), has no common factor with a(n-2), and does not share a 1-bit in its binary expansion with a(n-2).

1, 2, 6, 21, 161, 736, 66, 15, 145, 464, 68, 527, 155, 80, 96, 33, 143, 26, 48, 165, 65, 338, 14, 133, 209, 88, 10, 35, 273, 24, 40, 295, 531, 144, 136, 1037, 305, 50, 74, 333, 129, 688, 20, 325, 299, 138, 132, 341, 1147, 1184, 384, 261, 551, 608, 72, 141, 517, 770, 18, 57, 589, 1798, 34, 8313

Offset: 1

Author

Scott R. Shannon, May 26 2022

Keywords

• nonn

Comments

The sequence is similar to A336957 but with the addition restrictions that each new term a(n) must share a 1-bit in its binary expansion with a(n-1), while sharing no 1-bits with the binary expansion of a(n-2). To ensure the sequence is infinite each a(n) must not only have a prime factor not in a(n-1), implying no prime or prime powers can occur (see A336957), it must also have a 1-bit in its binary expansion that is a 0-bit in the binary expansion of a(n-1).

Examples

			a(5) = 161 = 10100001_2 as a(4) = 21 = 10101_2, a(3) = 6 = 110_2, and 161 is the smallest unused number that shares a factor with 21, has a 1-bit in common with 21 in their binary expansions, does not share a factor with 6, has no 1-bit in common with 6 in their binary expansions, has a prime factor not in 21, and has a 1-bit in its binary expansion that is a 0-bit in the binary expansion of 21.
		

Crossrefs

Cf. A336957, A353989, A354087, A064413, A352763.