

A216849


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


0



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
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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



