A352774 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not appeared that does not share a factor with a(n-2) + a(n-1) or a(n-2)*a(n-1).

1, 2, 5, 3, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 9, 35, 41, 27, 43, 47, 49, 53, 55, 59, 61, 67, 15, 71, 73, 65, 77, 51, 79, 83, 85, 89, 91, 97, 33, 101, 95, 39, 103, 107, 109, 113, 115, 119, 121, 127, 21, 125, 131, 57, 137, 139, 133, 45, 143, 149, 63, 145, 151, 69, 157, 155, 161, 81, 163, 167

Offset: 1

Author

Scott R. Shannon, Apr 02 2022

Keywords

• nonn

Comments

As a(2) is even, which forces a(3) and a(4) to be odd, all following terms will be odd as the sum of two odd terms is even. Beyond a(5) = 7 all subsequent primes appear in their natural order.

Examples

			a(2) = 5 as a(1) + a(2) = 3, a(1)*a(2) = 2, and 5 is the smallest unused number that does not share a factor with 3 or 2.
		

Links

• Scott R. Shannon, Image of the first 5000 terms. The green line is y = n.

Crossrefs

Cf. A352768, A352790, A332301, A351001, A349493, A251622.