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A178082 Numbers k for which 5*k-4, 5*k-2, 5*k+2, and 5*k+4 are primes.

%I A178082 #25 Apr 04 2025 15:02:17
%S A178082 3,21,39,165,297,375,417,651,693,1131,1887,2601,3129,3147,3213,3609,
%T A178082 3783,3885,4203,4455,5061,6345,6969,8757,10269,11067,12597,13443,
%U A178082 13899,14445,15453,15939,16209,16545,17763,19569,19827,20223,21969,23307
%N A178082 Numbers k for which 5*k-4, 5*k-2, 5*k+2, and 5*k+4 are primes.
%H A178082 Vincenzo Librandi, <a href="/A178082/b178082.txt">Table of n, a(n) for n = 1..1000</a>
%F A178082 a(n) = A173037(n+1)/5.
%e A178082 The associated prime quadruplets start as:
%e A178082      11,    13,    17,    19;   (for n =  3)
%e A178082     101,   103,   107,   109;   (for n = 21)
%e A178082     191,   193,   197,   199;   (for n = 39)
%e A178082     821,   823,   827,   829;
%e A178082    1481,  1483,  1487,  1489;
%e A178082    1871,  1873,  1877,  1879;
%e A178082    2081,  2083,  2087,  2089;
%e A178082    3251,  3253,  3257,  3259;
%e A178082    3461,  3463,  3467,  3469;
%e A178082    5651,  5653,  5657,  5659;
%e A178082    9431,  9433,  9437,  9439;
%e A178082   13001, 13003, 13007, 13009;
%e A178082   15641, 15643, 15647, 15649;
%e A178082   15731, 15733, 15737, 15739;
%e A178082   16061, 16063, 16067, 16069;
%e A178082   18041, 18043, 18047, 18049;
%e A178082   18911, 18913, 18917, 18919;
%e A178082   19421, 19423, 19427, 19429.
%t A178082 Flatten[Table[If[PrimeQ[5*n + 2] && PrimeQ[5*n - 2] && PrimeQ[5*n + 4] && PrimeQ[5*n - 4], n, {}], {n, 0, 10000}]]
%t A178082 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 A178082 (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 A178082 Cf. A007811, A024897, A024896.
%K A178082 nonn,easy
%O A178082 1,1
%A A178082 _Roger L. Bagula_, May 19 2010