A247271 Numbers n such that n^2+1 and 2*n^2+1 are both prime numbers.

1, 6, 24, 36, 66, 156, 204, 240, 264, 300, 306, 474, 570, 636, 750, 864, 936, 960, 1146, 1176, 1290, 1494, 1524, 1716, 1974, 2034, 2136, 2310, 2406, 2706, 2736, 2964, 3156, 3240, 3624, 3756, 3774, 3900, 3984, 4026, 4080, 4524, 4530, 4554, 4590, 4644, 4650, 4716

Offset

1,2

Comments

Numbers n such that A002522(n) and A058331(n) are prime numbers.

a(n)==0 mod 6 because the primes n^2+1 and 2*n^2+1 are congruent to 1 (mod 6).

The corresponding pairs of primes (n^2+1,2*n^2+1) are (2,3), (37,73), (577, 1153), (1297,2593), (4357,8713), (24337,48673), ...

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

a(2)=6 because A002522(6)=37 and A058331(6)=73 are both prime numbers.

Maple

A247271:=n->`if`(isprime(n^2+1) and isprime(2*n^2+1), n, NULL): seq(A247271(n), n=1..10^4); # Wesley Ivan Hurt, Sep 12 2014

Mathematica

lst={}; Do[p=n^2+1; q=2n^2+1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 5000}]; lst

Prog

(PARI)
for(n=1, 10^4, if(isprime(n^2+1)&&isprime(2*n^2+1), print1(n, ", "))) \\ Derek Orr, Sep 11 2014
(Magma) [n: n in [0..5000] | IsPrime(n^2+1) and IsPrime(2*n^2+1)]; // Vincenzo Librandi, Sep 14 2014

Crossrefs

Cf. A002496, A090698, A002522, A058331.

Sequence in context: A128459 A229292 A147826 * A065743 A225363 A230328

Adjacent sequences: A247268 A247269 A247270 * A247272 A247273 A247274

Keyword

nonn,easy

Author

Michel Lagneau, Sep 11 2014

Status

approved