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A247271 Numbers n such that n^2+1 and 2*n^2+1 are both prime numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 16 04:19 EST 2018. Contains 318158 sequences. (Running on oeis4.)