A354420 Lexicographically earliest infinite sequence of distinct positive numbers such that, for n>3, a(n) has a common factor with a(n-2), shares a 1-bit in its binary expansion with a(n-2), has no common factor with a(n-1), and does not share a 1-bit in its binary expansion with a(n-1).

1, 2, 5, 18, 65, 6, 25, 4, 35, 12, 49, 8, 7, 24, 133, 10, 21, 34, 9, 22, 105, 16, 3, 20, 33, 14, 81, 38, 129, 26, 69, 40, 23, 32, 207, 304, 15, 112, 135, 56, 195, 28, 99, 136, 39, 88, 261, 50, 141, 80, 47, 64, 423, 584, 51, 76, 17, 36, 323, 44, 19, 68, 57, 70, 153, 98, 285, 194, 45, 82, 165

Offset: 1

Author

Scott R. Shannon, May 26 2022

Keywords

• nonn

Comments

The sequence is similar to A098550 but with the addition restrictions that each new term a(n) must share a 1-bit in its binary expansion with a(n-2), while sharing no 1-bits with the binary expansion of a(n-1). Unlike A351691 no additional restrictions on the factors or 1-bits of a(n) are required for the sequence to be infinite. The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(5) = 65 = 1000001_2 as a(4) = 18 = 10010_2, a(3) = 5 = 101_2, and 65 is the smallest unused number that shares a factor with 5, has a 1-bit in common with 5 in their binary expansions, does not share a factor with 18, has no 1-bit in common with 18 in their binary expansions.
		

Crossrefs

Cf. A098550, A351691, A064413, A353990, A336957, A353989, A354087, A352763.