A363576 a(1) = 1, a(2) = 6; for n > 2, a(n) is the smallest positive number that has not yet appeared such that a(n) has a common factor with a(n-1), has no common factor with a(n-2), while the difference |a(n) - a(n-1)| is distinct from all previous differences |a(i) - a(i-1)|, i=2..n-1.

1, 6, 10, 35, 21, 12, 20, 55, 33, 18, 28, 77, 143, 26, 14, 105, 51, 34, 40, 95, 57, 24, 22, 187, 85, 15, 36, 52, 65, 45, 42, 68, 221, 39, 63, 56, 38, 171, 75, 115, 46, 74, 111, 69, 92, 44, 165, 87, 58, 88, 99, 135, 50, 82, 123, 183, 122, 70, 133, 209, 66, 93, 155, 80, 114, 153, 391, 161, 84

Offset: 1

Author

Scott R. Shannon, Jun 10 2023

Keywords

• nonn

Comments

This is a variation of A360519 where the difference between consecutive terms is distinct. See A360519 for further details.

In the first 100000 terms the only fixed points are 1, 585 and 3619, although it is possible more exist.

Examples

			a(11) = 28 as 28 shares 2 as a common factor with a(10) = 18 while sharing no common factor with a(9) = 33. Also the difference |28 - 18| = 10 is distinct from all previous differences. This is the first term to differ from A360519.
		

Links

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

Crossrefs

Cf. A360519, A361102, A098550, A336957.