A375889 a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest unused positive number such that a(n) shares a factor with a(n-1) and (a(n) AND a(n-1)) = min(a(n), a(n-1)), where AND is the binary AND operation.

1, 3, 15, 5, 45, 9, 27, 18, 2, 6, 4, 12, 8, 10, 14, 30, 16, 20, 22, 54, 32, 34, 38, 36, 39, 33, 51, 17, 85, 65, 75, 66, 64, 68, 70, 78, 72, 74, 90, 24, 26, 58, 40, 42, 46, 44, 60, 28, 62, 48, 50, 55, 35, 63, 7, 119, 21, 87, 69, 93, 81, 117, 52, 116, 80, 82, 86, 84, 92, 76, 94, 88, 120, 56, 122, 96

Offset: 1

Author

Scott R. Shannon, Sep 01 2024

Keywords

• nonn

Comments

The fixed points begin 1, 12, 284, 50726, 50764, 50770, 50772, 50811, although there are likely more.

The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(4) = 5 as 5 shares a factor with a(3) = 15 and min(15,5) = 5 and (5 AND 15) = 101_2 AND 1111_2 = 101_2 = 5.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A375890, A303767, A169837, A027750.