A222960 Numbers n such that 2*n + {3, 5, 9, 11} are all primes.

1, 4, 49, 94, 409, 739, 934, 1039, 1624, 1729, 2824, 4714, 6499, 7819, 7864, 8029, 9019, 9454, 9709, 10504, 11134, 12649, 15859, 17419, 21889, 25669, 27664, 31489, 33604, 34744, 36109, 38629, 39844, 40519, 41359, 44404

Offset: 1

Author

Vincenzo Librandi, Mar 13 2013

Keywords

• nonn
• easy

Comments

After 1, a(n) is congruent to 4 or 9 (mod 10), this means that a(n) is of the form 5k-1. Clearly, each term is not divisible by 3 and 11.

Links

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

Crossrefs

Cf. A007530, A136162.

Programs

Magma

[n: n in [1..50000] | forall{2*n+k: k in [3,5,9,11] | IsPrime(2*n+k)}];

Mathematica

Select[Range[50000], Union[PrimeQ[2 # + {3, 5, 9, 11}]]=={True}&]

Formula

a(n) = (A007530(n)-3)/2. [Michael B. Porter, Mar 21 2013]