A216849 Integers n such that both 2*n^2 + 3*(n+2)^2 and 3*n^2 + 2*(n+2)^2 are prime.

5, 257, 881, 1013, 1055, 1133, 1211, 1475, 1517, 1715, 1721, 2771, 2903, 2981, 3491, 3821, 4577, 4661, 4751, 4907, 5171, 5795, 6293, 6347, 6473, 6557, 6677, 7481, 7775, 8393, 8645, 8951, 9413, 9701, 9827, 9905, 10121, 10241, 10751, 10883, 10955, 11045, 11177

Offset

1,1

Comments

Sequence is infinite assuming Schinzel's hypothesis H. - Charles R Greathouse IV, Dec 10 2012

Links

Table of n, a(n) for n=1..43.

Example

2*5^2+3*7^2 = 197 and 2*7^2+3*5^2 = 173 are prime.

Mathematica

Select[Range[20000], PrimeQ[2*#^2 + 3*(# + 2)^2] && PrimeQ[3*#^2 + 2*(# + 2)^2] &] (* T. D. Noe, Dec 10 2012 *)

Prog

(PARI) for(a=1, 10000, c=a^2; b=(a+2)^2; if(isprime(2*c+3*b) && isprime(2*b+3*c), print1(a", ")))

Crossrefs

Sequence in context: A181397 A283039 A055386 * A201606 A139000 A061959

Adjacent sequences: A216846 A216847 A216848 * A216850 A216851 A216852

Keyword

nonn

Author

Zak Seidov, Dec 10 2012

Status

approved