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

All terms == 5 (mod 6). - Robert Israel, May 11 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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

Maple

filter:= n -> isprime(2*n^2 + 3*(n+2)^2) and isprime(3*n^2 + 2*(n+2)^2):
select(filter, [seq(i, i=5..10^5, 6)]); # Robert Israel, May 11 2025

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