login
Numbers k with the property that p = 2k + 1 and q = (2k)^3 + 3 are both primes.
0

%I #11 Sep 08 2022 08:45:38

%S 1,2,8,11,26,50,53,83,95,140,215,233,251,308,341,350,380,440,443,491,

%T 590,641,893,935,938,953,956,986,998,1040,1055,1103,1106,1220,1295,

%U 1430,1451,1478,1505,1511,1568,1583,1628,1778,1808,1898,1910,1916,1958,2006

%N Numbers k with the property that p = 2k + 1 and q = (2k)^3 + 3 are both primes.

%C Intersection of A005097 with the sequence of halved terms of A049441. - _R. J. Mathar_, Nov 05 2008

%e {n, p, q}: {1, 3, 11}, {2, 5, 67}, {8, 17, 4099}, {11, 23, 10651}, {26, 53, 140611}, {50, 101, 1000003}, {53, 107, 1191019}, {83, 167, 4574299}, {95, 191, 6859003}.

%o (Magma) [n: n in [0..10000]|IsPrime((2*n)+1) and IsPrime((2*n)^3+3)] // _Vincenzo Librandi_, Dec 13 2010

%Y Cf. A005097, A049441.

%K nonn

%O 1,2

%A _Zak Seidov_, Oct 30 2008