A353990 -id:A353990 - cp's OEIS frontend

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

Scott R. Shannon, May 26 2022

nonn

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.

			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.

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

cp's OEIS Frontend

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).

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