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

1,2

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.

Links

Table of n, a(n) for n=1..70.

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

Example

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.

Crossrefs

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

Sequence in context: A159016 A289108 A246364 * A083190 A171026 A064359

Adjacent sequences: A352771 A352772 A352773 * A352775 A352776 A352777

Keyword

nonn

Author

Scott R. Shannon, Apr 02 2022

Status

approved