A354803 a(1) = 1; for n > 1, a(n) is the smallest positive number that is coprime to a(n-1) and the product a(n) * a(n-1) is distinct from all previous products a(i) * a(i-1), i=2..n-1.

1, 1, 2, 3, 1, 4, 3, 5, 1, 7, 2, 5, 4, 7, 3, 8, 1, 9, 2, 11, 1, 13, 2, 15, 4, 9, 5, 7, 6, 11, 3, 13, 4, 11, 5, 8, 7, 9, 8, 11, 7, 10, 9, 11, 10, 13, 5, 16, 1, 17, 2, 19, 1, 23, 2, 25, 1, 27, 2, 29, 1, 31, 2, 37, 1, 32, 3, 16, 7, 12, 11, 13, 6, 17, 3, 19, 4, 17, 5, 19, 6, 23, 3, 25, 4, 23

Offset: 1

Author

Scott R. Shannon, Jun 07 2022

Keywords

• nonn
• look

Comments

This sequences uses similar a similar rule to A088177 but here all neighboring terms are coprime. In the first 1000000 terms the only fixed point is the first term while the smallest number not to have appeared is 2054. The sequence is conjectured to be a permutation of the positive integers.

See A354804 for the products of all pairs of terms.

Examples

			a(5) = 1 as a(4) = 3 and 1 is the smallest positive number that is coprime to 3 and whose product with 3, 1 * 3 = 3, has not previously appeared.
		

Links

• Scott R. Shannon, Image of the first 500000 terms.

Crossrefs

Cf. A354804, A354749, A354759, A354753, A354754, A088177, A317024.