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A178082 Numbers k for which 5*k-4, 5*k-2, 5*k+2, and 5*k+4 are primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 13 17:37 EDT 2022. Contains 356107 sequences. (Running on oeis4.)