A249446 Numbers n such that 2*(n^2-1) - 1 and 2*(n^2-1) + 1 are primes.
2, 4, 10, 11, 34, 41, 46, 49, 56, 59, 76, 85, 95, 125, 160, 181, 185, 196, 200, 206, 220, 245, 266, 280, 295, 301, 304, 346, 365, 379, 386, 391, 440, 470, 505, 556, 571, 595, 659, 679, 689, 731, 784, 815, 820, 854, 869, 896, 944, 959, 994, 1001, 1004, 1015, 1025, 1154, 1250, 1345, 1376
Offset: 1
Keywords
Examples
2 is in this sequence because 2*(2^2-1) - 1 = 5 and 2*(2^2-1) + 1 = 7 are both prime.
Links
- Colin Barker, Table of n, a(n) for n = 1..1600
Programs
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Magma
[ n: n in [1..1400] | IsPrime(2*(n^2-1)-1) and IsPrime(2*(n^2-1)+1) ];
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Maple
select(n -> isprime(2*n^2-3) and isprime(2*n^2-1), [$1 .. 10000]); # Robert Israel, Nov 18 2014
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Mathematica
Select[Range[0, 1500], PrimeQ[2 #^2 - 3] && PrimeQ[2 #^2 - 1] &] (* Vincenzo Librandi, Oct 29 2014 *)
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PARI
isok(n) = isprime(2*(n^2-1) - 1) && isprime(2*(n^2-1) + 1); \\ Michel Marcus, Oct 31 2014
Comments