A363504 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 prime(Omega(a(n-1))).

1, 2, 4, 3, 6, 9, 12, 5, 8, 10, 15, 18, 20, 25, 21, 24, 7, 14, 27, 30, 35, 33, 36, 28, 40, 42, 45, 50, 55, 39, 48, 11, 16, 49, 51, 54, 56, 63, 60, 70, 65, 57, 66, 75, 80, 22, 69, 72, 44, 85, 78, 90, 77, 81, 84, 91, 87, 93, 96, 13, 26, 99, 95, 102, 100, 98, 105, 110, 115, 108, 88, 112, 121, 111

Offset: 1

Author

Scott R. Shannon, Jun 06 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(371221) = 61. After the first two terms the fixed points in the first 500000 terms are 10, 26076, 26151, 26223, 26307, 26379, 26406, although it is possible more exist.

Examples

			a(8) = 5 as prime(Omega(a(7))) = prime(A001222(12)) = prime(3) = 5, and 5 is the smallest unused number that is a multiple of 5.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 500000 terms. The green line is a(n) = n.

Crossrefs

Cf. A363956, A001222, A000040, A351495.