A369272 a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide n*a(n-1).

1, 3, 2, 6, 7, 5, 4, 9, 8, 12, 10, 14, 15, 11, 16, 18, 20, 21, 22, 24, 25, 27, 26, 30, 28, 33, 32, 36, 35, 44, 39, 40, 42, 45, 34, 50, 48, 55, 38, 51, 46, 60, 49, 54, 56, 57, 52, 65, 58, 63, 62, 66, 70, 77, 64, 69, 68, 72, 75, 84, 80, 78, 85, 81, 74, 90, 91, 87, 76, 93, 82, 95, 86, 96, 98, 99

Offset: 1

Author

Scott R. Shannon, Jan 18 2024

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(63784) = 23.

Examples

			a(7) = 4 as 2 is the smallest prime that does not divide a(6)*7 = 5*7 = 35, and 4 = 2*2 is the smallest multiple of 2 that has not yet appeared.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Crossrefs

Cf. A369271, A351495, A053669.