A127845 Numbers k such that k^2 + 5 and k^2 + 7 are twin primes.

0, 6, 12, 36, 48, 78, 114, 162, 258, 414, 666, 792, 804, 996, 1044, 1206, 1308, 1314, 1356, 1548, 1584, 1632, 1734, 1902, 2106, 2196, 2214, 2346, 2358, 2592, 2634, 2766, 2808, 2868, 2892, 2988, 3072, 3246, 3432, 3516, 3576, 3774, 3894, 3912, 3996, 4038

Offset: 1

Author

Zak Seidov, Apr 05 2007

Keywords

• nonn

Comments

All terms are multiples of 6. Intersection of A114270 and A078402.

Links

• Robert Israel, Table of n, a(n) for n = 1..7640

Crossrefs

Cf. A078402, A114270.

Programs

Magma

[n: n in [0..500] | IsPrime(n^2+5) and IsPrime(n^2+7)] // Vincenzo Librandi, Nov 23 2010

Maple

filter:= n -> isprime(n^2+5) and isprime(n^2+7):
N:= 10000: # to get all entries <= 6*N
A127845:= select(filter, [6*n $ n=0..N]); # Robert Israel, Apr 17 2014

Mathematica

Select[Range[0,5000,6],AllTrue[#^2+{5,7},PrimeQ]&] (* Harvey P. Dale, May 25 2023 *)