A115272 Primes p such that p + 2, 18*p^2 + 1, and 18*(p+2)^2 + 1 are all primes.

29, 107, 431, 1487, 1607, 2141, 5501, 10139, 10271, 17579, 22481, 23057, 27479, 32369, 36341, 36929, 38447, 55931, 57527, 69827, 75539, 78539, 79691, 81047, 81971, 84179, 86027, 89561, 93761, 102059, 112571, 113147, 118799, 119687

Offset: 1

Author

Zak Seidov, Jan 19 2006

Keywords

• nonn

Examples

			a(1)=29 because 31, 18*29^2 + 1 = 15139, and 18*31^2 + 1 = 17299 are all primes.
		

Crossrefs

Cf. A089001 (Numbers n such that 2*n^2 + 1 is prime),

A090612 (Numbers k such that the k-th prime is of the form 2*k^2+1),

A090698 (Primes of the form 2*n^2+1),

A113541 (Numbers n such that 18*n^2+1 is a multiple of 19).

Programs

Magma

[p: p in PrimesUpTo(200000)| IsPrime(p+2) and IsPrime(18*p^2+1) and IsPrime(18*(p+2)^2+1)] // Vincenzo Librandi, Nov 13 2010

Extensions

More terms from Vincenzo Librandi, Mar 27 2010