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
Examples
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.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Programs
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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
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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 *)
Formula
a(n) = A173037(n+1)/5.