A229065 - OEIS

%I #31 Sep 08 2022 08:46:05

%S 5,7,19,67,1027,4099,65539,262147,4194307,268435459,1073741827,

%T 68719476739,1099511627779,4398046511107,70368744177667,

%U 4503599627370499,288230376151711747,1152921504606846979,73786976294838206467,1180591620717411303427,4722366482869645213699

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

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

%C 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.

%H Vincenzo Librandi, <a href="/A229065/b229065.txt">Table of n, a(n) for n = 1..200</a>

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

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

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

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Sep 17 2013