A361825 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide a(n-2) + a(n-1).

1, 2, 4, 5, 6, 8, 3, 10, 12, 9, 14, 16, 7, 18, 20, 15, 22, 24, 21, 26, 28, 25, 30, 32, 27, 34, 36, 33, 38, 40, 35, 42, 44, 39, 46, 48, 45, 50, 52, 55, 54, 56, 51, 58, 60, 57, 62, 64, 65, 66, 68, 63, 70, 72, 69, 74, 76, 49, 78, 80, 75, 82, 84, 81, 86, 88, 85, 90, 92, 87, 94, 96, 93, 98, 100, 95

Offset: 1

Author

Scott R. Shannon, Mar 25 2023

Keywords

• nonn

Comments

The sequence is conjectured to be a permutation of the positive integers, although it takes many terms for the primes to appear, e.g., a(191443) = 19.

Examples

			a(3) = 4 as a(1) + a(2) = 1 + 2 = 3 which does not contain 2 as a prime factor, and 4 is the smallest unused number that is a multiple of 2.
a(4) = 5 as a(2) + a(3) = 2 + 4 = 6 = 2*3 which does not contain 5 as a prime factor, and 5 is the smallest unused number that is a multiple of 5.
		

Links

• Scott R. Shannon, Image of the first 50000 terms. The green line is a(n) = n.

Crossrefs

Cf. A351495, A359804, A353026, A352793.