A350472 Positive integers k such that if p is the next prime > k, and q is the previous prime < k, then p - k is prime and k - q is prime.

5, 9, 15, 21, 26, 34, 39, 45, 50, 56, 64, 69, 76, 81, 86, 92, 94, 99, 105, 111, 116, 120, 124, 129, 134, 142, 144, 146, 154, 160, 165, 170, 176, 184, 186, 188, 195, 204, 206, 216, 218, 225, 231, 236, 244, 246, 248, 254, 260, 266, 274, 279, 286, 288, 290, 296

Offset: 1

Author

Ryan Bresler, Jan 01 2022

Keywords

• nonn

Comments

a(n) can only be composite (excluding a(1) = 5).

Examples

			9 is a term because the next prime > 9 is 11 and the previous prime < 9 is 7, and 11 - 9 = 2 (which is prime) and 9 - 7 = 2 (which is also prime).
		

Crossrefs

Intersection of A350496 and A350460.

Cf. A175090, A225461.

Programs

Maple

q:= n-> andmap(isprime, [nextprime(n)-n, n-prevprime(n)]):
select(q, [$3..400])[];  # Alois P. Heinz, Jan 01 2022

Mathematica

Select[Range[350], And @@ PrimeQ[{# - NextPrime[#, -1], NextPrime[#] - #}] &] (* Amiram Eldar, Jan 01 2022 *)

PARI

isok(k) = my(p=nextprime(k+1), q=precprime(k-1)); isprime(p-k) && isprime(k-q); \\ Michel Marcus, Jan 01 2022

Python

from sympy import isprime, nextprime, prevprime
def ok(n):
    return n > 2 and isprime(nextprime(n) - n) and isprime(n - prevprime(n))
print([k for k in range(341) if ok(k)]) # Michael S. Branicky, Jan 01 2022