A105652 Numbers k such that p1=2k+3, p2=4k+5 and p3=6k+7 are all prime.

0, 2, 17, 104, 134, 152, 164, 167, 299, 362, 584, 617, 647, 764, 827, 1109, 1139, 1277, 1517, 1529, 1532, 2129, 2222, 2399, 2474, 2612, 2789, 2924, 3074, 3179, 3344, 3419, 3482, 3809, 3839, 3842, 3932, 4007, 4082, 4094, 4142, 4259, 4262, 4322, 4469, 4544

Offset: 1

Author

Zak Seidov, Apr 16 2005

Keywords

• nonn

Comments

Except for 0, all terms == 2 or 14 (mod 15). - Robert Israel, Jun 08 2018

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005382, A005383, A105610, A105653 - A105657, A174734.

Programs

Magma

[n: n in [0..5000] | IsPrime(2*n+3) and IsPrime(4*n+5) and IsPrime(6*n+7)]; // Vincenzo Librandi, Nov 13 2010

Maple

select(k -> andmap(isprime, [2*k+3,4*k+5,6*k+7]), [0, seq(seq(15*i+j,j=[2,14]),i=0..1000)]); # Robert Israel, Jun 08 2018

Formula

a(n) = (A174734(n)-3)/2. - Robert Israel, Jun 08 2018