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A242327 Primes p for which (p^n) + 2 is prime for n = 1, 3, 5, and 7. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A319063 A015407 A204536

Adjacent sequences:  A242324 A242325 A242326 * A242328 A242329 A242330

KEYWORD

nonn

AUTHOR

Abhiram R Devesh, May 10 2014

STATUS

approved

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Last modified September 27 00:14 EDT 2020. Contains 337378 sequences. (Running on oeis4.)