A247147 Numbers k such that 3*k-4 and 2^k-1 are prime.

2, 3, 5, 7, 17, 19, 31, 61, 89, 107, 521, 1279, 9689, 9941, 21701, 23209, 216091, 13466917, 30402457, 57885161

Offset: 1

Author

Vincenzo Librandi, Nov 21 2014

Keywords

• nonn
• more

Comments

All terms are primes.

Links

• Ben Green and Terence Tao, The primes contain arbitrarily long arithmetic progressions, arXiv:math/0404188 [math.NT], 2004-2007; Annals of Mathematics, 167 (2008), pp. 481-547.

Crossrefs

Cf. A000043, A001348, A228121.

Programs

Magma

[n: n in [0..10000] | IsPrime(3*n-4) and IsPrime(2^n-1)];

Mathematica

Select[Range[10000], PrimeQ[2^# - 1] && PrimeQ[3 # - 4] &]

Python

from sympy import isprime
from itertools import count, islice
def agen(startk=1):
    for k in count(startk):
        if isprime(3*k-4) and isprime(2**k-1):
            yield k
print(list(islice(agen(), 12))) # Michael S. Branicky, Jul 31 2022

Extensions

a(20) using A000043 from Michael S. Branicky, Jul 31 2022