A347619 Earliest sequence of integers > 1 such that gcd(a(n),a(n+k)) = 1, where k = 1..a(n-1), with a(1) = 1 and a(2) = 2.

1, 2, 3, 2, 5, 3, 7, 2, 5, 11, 7, 3, 5, 13, 17, 2, 5, 11, 19, 3, 5, 13, 7, 11, 5, 23, 29, 13, 17, 31, 19, 11, 23, 2, 37, 41, 5, 7, 37, 3, 43, 47, 17, 7, 23, 43, 37, 31, 53, 59, 29, 11, 23, 61, 67, 71, 73, 2, 13, 79, 83, 7, 13, 19, 23, 89, 97, 101, 103, 43, 13, 107, 109, 41, 79, 113, 127, 3, 5

Offset: 1

Author

Scott R. Shannon, Sep 09 2021

Keywords

• nonn

Comments

As the sequence always takes the earliest number satisfying the restriction gcd(a(n),a(n+k)) = 1, all the terms beyond a(1) will be prime.

Examples

			a(3) = 3, as a(1) = 1, a(2) = 2, so the next one term after a(2) cannot share a divisor with 2, and the smallest such number is 3.
a(4) = 2 and a(5) = 5, as a(2) = 2, a(3) = 3, so the next two terms after a(3) cannot share a divisor with 3. The first such term is 2. But now a(3) = 3 and a(4) = 2, so the next three terms after a(4) cannot share a divisor with 2. The smallest number which satisfies both of these restrictions is 5.
		

Crossrefs

Cf. A000040, A027749.