The On-Line Encyclopedia of Integer Sequences (OEIS)

A225431 revision #32

A225431

Primes p such that there is a prime q satisfying 3*p^2 - q^2 = 2.

3, 11, 41, 2131, 110771, 15558008491

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes q: 5, 19, 71, 3691, 191861,...

(q - p)/2: 1, 4, 15, 780, 40545,...

a(7) > 2.8016852867294*10^4857. - Zak Seidov, May 09 2013

Probably finite.

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

11 is prime and sqrt(3*11^2 - 2) = sqrt(361) = 19 is prime, so 11 is in the sequence.

PROG

(PARI) v=[1, 1]; for(i=1, 1e4, v=[v[2], 4*v[2]-v[1]]; if(ispseudoprime(v[2]) && ispseudoprime(sqrtint(3*v[2]^2-2)), print1(v[2]", "))) \\ Charles R Greathouse IV, May 13 2013

(PFGW)

ABC2 Linear(3, 11, 41, 153, $a) & Linear(5, 19, 71, 265, $a)

a: from 3 to 20000 // Charles R Greathouse IV, May 13 2013

CROSSREFS

Sequence in context: A102417 A358426 A096147 * A359248 A099489 A077830

Adjacent sequences: A225428 A225429 A225430 * A225432 A225433 A225434

KEYWORD

nonn

AUTHOR

Irina Gerasimova, May 07 2013

EXTENSIONS

a(4) from R. J. Mathar, May 07 2013

a(6) from Charles R Greathouse IV, May 07 2013

a(5) from Zak Seidov, May 09 2013

STATUS

reviewed