A318239 a(n) is the smallest primitive root of A133433(n).

2, 3, 5, 6, 7, 10, 11, 12, 18, 20, 24, 40, 42, 45, 48, 54, 72, 80, 96

Offset: 1

Author

Jianing Song, Aug 22 2018

Keywords

• nonn
• hard
• more

Comments

Also with an initial 1, numbers k such that A023048(k) set a new record.

If A023048(108) != 0 (which is implied assuming generalized Artin's conjecture) then the next term of this sequence is 108.

Conjecturally 11 is the largest prime in this sequence, 42 is the largest squarefree term, and 45 is the largest odd term.

Examples

			The smallest prime with least primitive root 11 is 643, and the smallest prime with least primitive root 2, 3, 5, ..., 10 are all < 643, so 11 is a term.
The smallest prime with least primitive root 45 is 95525767, and the smallest prime with least primitive root 2, 3, 5, ..., 44 are all < 95525767, so 45 is a term.
13 is not a term since the smallest prime with least primitive root 13 is 457, but the smallest prime with least primitive root 12 is 4111, which is larger than 457.
		

Links

• Tomás Oliveira e Silva, Least primitive root of prime numbers

Crossrefs

Cf. A023048, A133433.