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

Author

Michel Lagneau, Sep 11 2014

Keywords

• nonn
• easy

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), ...

Examples

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

Links

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

Crossrefs

Cf. A002496, A090698, A002522, A058331.

Programs

Magma

[n: n in [0..5000] | IsPrime(n^2+1) and IsPrime(2*n^2+1)]; // Vincenzo Librandi, Sep 14 2014

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

PARI

for(n=1,10^4,if(isprime(n^2+1)&&isprime(2*n^2+1),print1(n,", "))) \\ Derek Orr, Sep 11 2014