A350927 a(1)=1, a(2)=2; for n > 2, a(n) is the smallest unused positive number such that gcd(a(n-1) * |a(n-1) - a(n-2)|, a(n)) > 1.

1, 2, 4, 6, 3, 9, 8, 10, 5, 15, 12, 14, 7, 21, 16, 18, 20, 22, 11, 33, 24, 26, 13, 39, 27, 28, 30, 25, 35, 32, 34, 17, 51, 36, 38, 19, 57, 40, 42, 44, 46, 23, 69, 45, 48, 50, 52, 54, 56, 49, 63, 58, 29, 87, 60, 55, 65, 62, 31, 93, 64, 66, 68, 70, 72, 74, 37, 111, 75, 76, 78, 80, 82, 41, 123, 81

Offset: 1

Author

Scott R. Shannon, Jan 28 2022

Keywords

• nonn

Comments

This is likely a permutation of the natural numbers. The sequence shows similar behavior to the EKG sequence A064413. In the first 500000 terms the fixed points are 1, 2, 77, 221, and it is likely no more exist.

Examples

			a(4) = 6 as a(3)*|a(3)-a(2)| = 4*2 = 8, 6 has not been used and gcd(6,8) > 1.
a(8) = 10 as a(7)*|a(7)-a(6)| = 8*1 = 8, 10 has not been used and gcd(10,8) > 1.
		

Links

• Scott R. Shannon, Image of the first 10000 terms. The green line is y = n.

Crossrefs

Cf. A351001, A337136, A064413, A336957, A098550, A089088, A251622.