A308316 Numbers m such that q = 2^m - 1 and r = m^2 + m + 1 are both primes.

2, 3, 5, 17, 89, 9689, 11213, 2976221

Offset

1,1

Comments

All terms are primes.

Mersenne exponents p from A000043 such that p^2 + p + 1 is a prime.

Intersection of A000043 and A002384.

Corresponding values of primes q: 3, 7, 31, 131071, 618970019642690137449562111, ...

Corresponding values of primes r: 7, 13, 31, 307, 8011, 93886411, 125742583, 8857894417063, ...

Links

Table of n, a(n) for n=1..8.

Prog

(Magma) [m: m in [1..1000] | IsPrime(2^m - 1)  and IsPrime(m^2 + m + 1)]
(PARI) isok(n) = isprime(2^n-1) && isprime(n^2+n+1); \\ Michel Marcus, May 21 2019

Crossrefs

Cf. A000043, A002383, A002384.

Sequence in context: A245641 A082979 A065952 * A089983 A370606 A072858

Adjacent sequences: A308313 A308314 A308315 * A308317 A308318 A308319

Keyword

nonn,more

Author

Jaroslav Krizek, May 19 2019

Status

approved