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A247271
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Numbers n such that n^2+1 and 2*n^2+1 are both prime numbers.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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), ...
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LINKS
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EXAMPLE
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a(2)=6 because A002522(6)=37 and A058331(6)=73 are both prime numbers.
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MAPLE
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MATHEMATICA
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lst={}; Do[p=n^2+1; q=2n^2+1; If[PrimeQ[p] && PrimeQ[q], AppendTo[lst, n]], {n, 5000}]; lst
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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