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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 July 12 16:06 EDT 2024. Contains 374251 sequences. (Running on oeis4.)