OFFSET
2,3
COMMENTS
By Dirichlet's theorem on arithmetic progressions, we know there exists a prime q of the form 2*k*p+1. But the theorem does not give us any information about the size of the smallest q. It is conjectured that q < p^2. Moreover, it seems that a(n) goes to infinity as n increases.
LINKS
Jianing Song, Table of n, a(n) for n = 2..10000
EXAMPLE
Let P denote the set of prime numbers. Then:
a(8) = #({39, 77, 115, 153, 191, 229, 267, 305, 343} intersect P) = #{191, 229} = 2.
a(11) = #({63, 125, 187, 249, 311, 373, 435, 497, 559, 621, 683, 745, 807, 869, 931} intersect P) = #{311, 373, 683} = 3.
PROG
(PARI) a(n) = my(p=prime(n)); sum(k=1, (p-1)/2, isprime(2*k*p+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Feb 21 2021
STATUS
approved