A354749 a(1) = 1; for n > 1, a(n) is the smallest positive number greater than 1 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, 2, 3, 4, 5, 2, 7, 3, 5, 6, 7, 4, 9, 2, 11, 3, 8, 5, 7, 8, 9, 5, 11, 4, 13, 2, 17, 3, 13, 5, 12, 7, 9, 10, 7, 11, 6, 13, 7, 15, 8, 11, 9, 13, 8, 17, 4, 19, 2, 23, 3, 16, 5, 17, 6, 19, 3, 25, 2, 27, 4, 23, 5, 19, 7, 16, 9, 14, 11, 10, 13, 11, 12, 13, 14, 15, 11, 16, 13, 15, 16, 17, 7, 20, 9

Offset: 1

Author

Scott R. Shannon, Jun 06 2022

Keywords

• nonn
• look

Comments

This is a variation of A354803 where all terms beyond the first must be greater than 1. In the first 1000000 terms the fixed points are 1,2,3,4,5,7, it is likely no more exist, while the smallest number not to have appeared is 2090. The sequence is conjectured to be a permutation of the positive integers.

See A354759 for the products of all pairs of terms.

Examples

			a(6) = 2 as a(5) = 5 and 2 is the smallest number greater than 1 that is coprime to 5 and whose product with 5, 2 * 5 = 10, has not previously appeared.
		

Links

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

Crossrefs

Cf. A354759, A354803, A354804, A354753, A354754, A088177.