A352101 The numbers formed by removing the required prime factors to form the number from a set which is initially empty and that has primes added via the addition of the missing prime factors of numbers which cannot be created from those currently in the set. Start by trying to create the number 2.

6, 10, 12, 20, 21, 22, 26, 30, 34, 35, 36, 38, 44, 46, 52, 58, 60, 63, 68, 70, 74, 76, 82, 84, 86, 90, 92, 93, 102, 104, 105, 106, 110, 114, 116, 118, 122, 126, 130, 132, 134, 136, 141, 142, 146, 148, 150, 154, 156, 161, 164, 166, 170, 171, 172, 178, 180, 182, 186, 194, 195, 198, 202, 203

Offset: 1

Author

Scott R. Shannon, May 06 2022

Keywords

• nonn

Comments

This sequence is a variation of A337486; instead of adding to the set all the prime factors of the numbers that cannot be created from the current primes in the set, only add those primes that are missing from the set, i.e., only add enough primes so that the number could then be created from the set. See A337486 for further details.

Examples

			a(1) = 6. As there are no primes initially in the set, the numbers 2, 3, 4, 5 cannot be created. These numbers add a 2, a 3, another 2 (only one extra 2 is added as 4 = 2*2 and one 2 is already in the set), and a 5. As there is now one 2 and one 3 the number 6 = 2*3 can be created. After 6 is created the set of primes now contains 2 and 5.
a(2) = 10. After 7, 8, 9, none of which can be created from the prime set, the prime set contains 2, 2, 2, 3, 3, 5, 7. Note 8 only added two extra 2's as one 2 was already in the set. As 2 and 5 are present 10 = 2*5 can be created, after which the set contains 2, 2, 3, 3, 7.
		

Crossrefs

Cf. A337486, A331276, A330430, A109895.