A359799 a(1) = 1, a(2) = 3; for n > 2, a(n) is the smallest positive number which has not appeared that shares a factor with |a(n-1) - 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, 3, 6, 12, 2, 10, 14, 26, 4, 11, 28, 17, 22, 35, 65, 5, 20, 36, 8, 32, 9, 23, 42, 76, 18, 38, 56, 15, 41, 16, 25, 54, 87, 21, 48, 27, 63, 24, 66, 7, 59, 13, 44, 93, 49, 84, 30, 62, 100, 19, 69, 106, 37, 90, 212, 34, 74, 122, 33, 89, 46, 129, 249, 39, 86, 141, 40, 101, 183, 50, 95, 159, 52

Offset: 1

Author

Scott R. Shannon, Mar 07 2023

Keywords

• nonn

Comments

In the first 100000 terms the only fixed point is a(1) = 1; it is unknown if more exist. The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(5) = 2 as |a(4) - a(3)| = |12 - 6| = 6, and 2 is the smallest unused number that shares a factor with 6 while the difference |2 - a(4)| = |2 - 12| = 10 is distinct from all previous differences.
		

Links

• Scott R. Shannon, Image for n = 1..100000. The green line is a(n) = n.

Crossrefs

Cf. A361314, A337136, A354755, A354727, A354687, A354753, A353989, A354087, A352763.