A229065 Numbers of the form 2^(p-1)+3, where p is prime.

5, 7, 19, 67, 1027, 4099, 65539, 262147, 4194307, 268435459, 1073741827, 68719476739, 1099511627779, 4398046511107, 70368744177667, 4503599627370499, 288230376151711747, 1152921504606846979, 73786976294838206467, 1180591620717411303427, 4722366482869645213699

Offset: 1

Author

Vincenzo Librandi, Sep 17 2013

Keywords

• nonn

Comments

Primes in the sequence: 5, 7, 19, 67, 4099, 65539, 262147, 268435459, 1073741827, ...

On the other hand, for example, 2^(p-1) + 3 is composite when p == 11 (mod 12) or p == 5 (mod 18), with p>5; or when p is of the form 2*h^2+2*h*(k+2)+3*k, with k>0 and h>1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A153503 (associated primes p), A098828, A057732, A057736.

Programs

Magma

[2^(p-1)+3:  p in PrimesUpTo(80)];

Mathematica

Table[2^(Prime[n] - 1) + 3, {n, 25}]