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

3, 21, 39, 165, 297, 375, 417, 651, 693, 1131, 1887, 2601, 3129, 3147, 3213, 3609, 3783, 3885, 4203, 4455, 5061, 6345, 6969, 8757, 10269, 11067, 12597, 13443, 13899, 14445, 15453, 15939, 16209, 16545, 17763, 19569, 19827, 20223, 21969, 23307

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

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

Example

The associated prime quadruplets start as:
.    11,    13,    17,    19;   (for n =  3)
.   101,   103,   107,   109;   (for n = 21)
.   191,   193,   197,   199;   (for n = 39)
.   821,   823,   827,   829;
.  1481,  1483,  1487,  1489;
.  1871,  1873,  1877,  1879;
.  2081,  2083,  2087,  2089;
.  3251,  3253,  3257,  3259;
.  3461,  3463,  3467,  3469;
.  5651,  5653,  5657,  5659;
.  9431,  9433,  9437,  9439;
. 13001, 13003, 13007, 13009;
. 15641, 15643, 15647, 15649;
. 15731, 15733, 15737, 15739;
. 16061, 16063, 16067, 16069;
. 18041, 18043, 18047, 18049;
. 18911, 18913, 18917, 18919;
. 19421, 19423, 19427, 19429.

Mathematica

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

Prog

(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

Crossrefs

Cf. A007811, A024897, A024896.

Sequence in context: A227241 A076169 A298035 * A056387 A056377 A146712

Adjacent sequences: A178079 A178080 A178081 * A178083 A178084 A178085

Keyword

nonn,easy

Author

Roger L. Bagula, May 19 2010

Status

approved