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

1,1

Links

Table of n, a(n) for n=1..34.

Example

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

Prog

(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

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).

Sequence in context: A233049 A233050 A142176 * A138716 A276776 A142194

Adjacent sequences: A115269 A115270 A115271 * A115273 A115274 A115275

Keyword

nonn

Author

Zak Seidov, Jan 19 2006

Extensions

More terms from Vincenzo Librandi, Mar 27 2010

Status

approved