A242327 Primes p for which (p^n) + 2 is prime for n = 1, 3, 5, and 7.

132749, 1175411, 3940799, 5278571, 11047709, 12390251, 15118769, 21967241, 22234871, 26568929, 31809959, 32229341, 32969591, 35760551, 38704661, 43124831, 43991081, 49248971, 50227211, 51140861, 53221631, 55568171, 59446109, 63671651, 71109161, 76675589

Offset

1,1

Comments

Subsequence of A001359 and A048637.

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..50

Example

p = 132749 (prime);
p + 2 = 132751 (prime);
p^3 + 2 = 2339342304585751 (prime);
p^5 + 2 = 41224584878413873150038751 (prime);
p^7 + 2 = 726471878470342746448722269536491751 (prime).

Prog

(Python)
import sympy
from sympy.ntheory import isprime, nextprime
n=2
while True:
    n1=n+2
    n2=n**3+2
    n3=n**5+2
    n4=n**7+2
    ##.Check if n1, n2, n3 and n4 are also primes
    if all(isprime(x) for x in [n1, n2, n3, n4]):
        print(n, ", ", n1, ", ", n2, ", ", n3, ", ", n4)
    n=nextprime(n)
(PARI) isok(p) = isprime(p) && isprime(p+2) && isprime(p^3+2) && isprime(p^5+2) && isprime(p^7+2); \\ Michel Marcus, May 15 2014
(Sage)
def is_A242327(n):
    return is_prime(n) and all([is_prime(n^(2*k+1)+2) for k in range(4)])
filter(is_A242327, range(3940800)) # Peter Luschny, May 15 2014

Crossrefs

Cf. A001359, A006512, A048637.

Sequence in context: A161356 A236735 A238233 * A339535 A319063 A344830

Adjacent sequences: A242324 A242325 A242326 * A242328 A242329 A242330

Keyword

nonn

Author

Abhiram R Devesh, May 10 2014

Status

approved