A359487 a(n) is the smallest start of a run of 2 or more integers having a prime factor greater than n.

2, 5, 10, 10, 13, 13, 22, 22, 22, 22, 37, 37, 37, 37, 37, 37, 37, 37, 46, 46, 46, 46, 58, 58, 58, 58, 58, 58, 61, 61, 73, 73, 73, 73, 73, 73, 82, 82, 82, 82, 106, 106, 106, 106, 106, 106, 106, 106, 106, 106, 106, 106, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157

Offset: 1

Author

Thomas Garrison, Jan 02 2023

Keywords

• nonn

Comments

Each term is a prime or one less than a prime.

Each even term is twice an odd prime (except for a(1)=2).

Each prime term is of the form 2p-1 where p is prime.

Examples

			For n=5, a(5) = 13 since the two numbers 13 and 14=2*7 both have a prime factor > n.
		

Crossrefs

Cf. A006530 (gpf), A359488 (run lengths).

Cf. A327909.

Programs

PARI

gpf(n) = vecmax(factor(n)[,1]); \\ A006530
a(n) = my(k=2); while(!((gpf(k)>n) && (gpf(k+1)>n)), k++); k; \\ Michel Marcus, Jan 10 2023

Formula

Conjecture: a(n) ~ 2*n.