

A237641


Primes p of the form n^2n1 (for prime n) such that p^2p1 is also prime.


3



5, 236681, 380071, 457651, 563249, 1441199, 1660231, 2491661, 3050261, 4106701, 5137021, 5146091, 5329171, 10617821, 15574861, 19860391, 20852921, 21349019, 21497131, 23025601, 24507449, 32495699, 36342811, 48867089, 51129649, 59082281
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Except a(1), all numbers are congruent to 1 mod 10 or 9 mod 10.
These are the primes in the sequence A237527.


LINKS

Table of n, a(n) for n=1..26.


EXAMPLE

5 = 3^23^11 (3 is prime) and 5^251 = 19 is prime. Since 5 is prime too, 5 is a member of this sequence.


PROG

(Python)
import sympy
from sympy import isprime
def poly2(x):
..if isprime(x):
....f = x**2x1
....if isprime(f**2f1):
......return True
..return False
x = 1
while x < 10**5:
..if poly2(x):
....if isprime(x**2x1):
......print(x**2x1)
..x += 1
(PARI)
s=[]; forprime(n=2, 40000, p=n^2n1; if(isprime(p) && isprime(p^2p1), s=concat(s, p))); s \\ Colin Barker, Feb 11 2014


CROSSREFS

Cf. A237527, A091567, A091568.
Sequence in context: A151589 A243114 A038027 * A057679 A123751 A152516
Adjacent sequences: A237638 A237639 A237640 * A237642 A237643 A237644


KEYWORD

nonn


AUTHOR

Derek Orr, Feb 10 2014


STATUS

approved



