login
A359487
a(n) is the smallest start of a run of 2 or more integers having a prime factor greater than n.
1
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
1,1
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.
FORMULA
Conjecture: a(n) ~ 2*n.
EXAMPLE
For n=5, a(5) = 13 since the two numbers 13 and 14=2*7 both have a prime factor > n.
PROG
(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
CROSSREFS
Cf. A006530 (gpf), A359488 (run lengths).
Cf. A327909.
Sequence in context: A258779 A097378 A078310 * A138848 A194350 A182179
KEYWORD
nonn
AUTHOR
Thomas Garrison, Jan 02 2023
STATUS
approved