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A237641 Primes p of the form n^2-n-1 (for prime n) such that p^2-p-1 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 = 3^2-3^1-1 (3 is prime) and 5^2-5-1 = 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**2-x-1

....if isprime(f**2-f-1):

......return True

..return False

x = 1

while x < 10**5:

..if poly2(x):

....if isprime(x**2-x-1):

......print(x**2-x-1)

..x += 1

(PARI)

s=[]; forprime(n=2, 40000, p=n^2-n-1; if(isprime(p) && isprime(p^2-p-1), 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

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Last modified December 12 06:05 EST 2017. Contains 295937 sequences.