A178082 - OEIS

%I #18 Sep 08 2022 08:45:53

%S 3,21,39,165,297,375,417,651,693,1131,1887,2601,3129,3147,3213,3609,

%T 3783,3885,4203,4455,5061,6345,6969,8757,10269,11067,12597,13443,

%U 13899,14445,15453,15939,16209,16545,17763,19569,19827,20223,21969,23307

%N Numbers k for which 5*k-4, 5*k-2, 5*k+2, and 5*k+4 are primes.

%H Vincenzo Librandi, <a href="/A178082/b178082.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A173037(n+1)/5.

%e The associated prime quadruplets start as:

%e .    11,    13,    17,    19;   (for n =  3)

%e .   101,   103,   107,   109;   (for n = 21)

%e .   191,   193,   197,   199;   (for n = 39)

%e .   821,   823,   827,   829;

%e .  1481,  1483,  1487,  1489;

%e .  1871,  1873,  1877,  1879;

%e .  2081,  2083,  2087,  2089;

%e .  3251,  3253,  3257,  3259;

%e .  3461,  3463,  3467,  3469;

%e .  5651,  5653,  5657,  5659;

%e .  9431,  9433,  9437,  9439;

%e . 13001, 13003, 13007, 13009;

%e . 15641, 15643, 15647, 15649;

%e . 15731, 15733, 15737, 15739;

%e . 16061, 16063, 16067, 16069;

%e . 18041, 18043, 18047, 18049;

%e . 18911, 18913, 18917, 18919;

%e . 19421, 19423, 19427, 19429.

%t Flatten[Table[If[PrimeQ[5*n + 2] && PrimeQ[5*n - 2] && PrimeQ[5*n + 4] && PrimeQ[5*n - 4], n, {}], {n, 0, 10000}]]

%t Select[Range[25000],AllTrue[5#+{4,2,-2,-4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 03 2018 *)

%o (Magma) [n: n in [0..1000]| IsPrime(5*n - 4) and IsPrime(5*n - 2) and IsPrime(5*n + 2) and IsPrime(5*n + 4)]; _Vincenzo Librandi_, Nov 30 2010

%Y Cf. A007811, A024897, A024896.

%K nonn,easy

%O 1,1

%A _Roger L. Bagula_, May 19 2010