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

%I A247271 #16 Sep 08 2022 08:46:09
%S A247271 1,6,24,36,66,156,204,240,264,300,306,474,570,636,750,864,936,960,
%T A247271 1146,1176,1290,1494,1524,1716,1974,2034,2136,2310,2406,2706,2736,
%U A247271 2964,3156,3240,3624,3756,3774,3900,3984,4026,4080,4524,4530,4554,4590,4644,4650,4716
%N A247271 Numbers n such that n^2+1 and 2*n^2+1 are both prime numbers.
%C A247271 Numbers n such that A002522(n) and A058331(n) are prime numbers.
%C A247271 a(n)==0 mod 6 because the primes n^2+1 and 2*n^2+1 are congruent to 1 (mod 6).
%C A247271 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), ...
%H A247271 Jens Kruse Andersen, <a href="/A247271/b247271.txt">Table of n, a(n) for n = 1..10000</a>
%e A247271 a(2)=6 because A002522(6)=37 and A058331(6)=73 are both prime numbers.
%p A247271 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
%t A247271 lst={}; Do[p=n^2+1; q=2n^2+1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 5000}]; lst
%o A247271 (PARI)
%o A247271 for(n=1,10^4,if(isprime(n^2+1)&&isprime(2*n^2+1),print1(n,", "))) \\ _Derek Orr_, Sep 11 2014
%o A247271 (Magma) [n: n in [0..5000] | IsPrime(n^2+1) and IsPrime(2*n^2+1)]; // _Vincenzo Librandi_, Sep 14 2014
%Y A247271 Cf. A002496, A090698, A002522, A058331.
%K A247271 nonn,easy
%O A247271 1,2
%A A247271 _Michel Lagneau_, Sep 11 2014