A088485 Numbers n such that n^2 + n - 1 and n^2 + n + 1 are twin primes.
2, 3, 5, 6, 8, 15, 20, 21, 24, 38, 41, 50, 54, 59, 66, 89, 101, 131, 138, 141, 153, 155, 164, 176, 188, 203, 206, 209, 215, 218, 231, 236, 246, 288, 290, 309, 314, 351, 378, 395, 405, 453, 455, 456, 495, 500, 518, 530, 551, 560, 624, 644, 668, 686, 720, 728, 743, 761, 798, 825, 890, 915, 950, 974, 981
Offset: 1
Examples
20*20 + 20 - 1 = 419, 419 and 421 twin primes, 20 is the 7th of the sequence
Links
- Pierre CAMI, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Programs
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Magma
[n: n in [1..2*10^3] |IsPrime(n^2+n-1) and IsPrime(n^2+n+1)]; // Vincenzo Librandi, Dec 26 2015
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Mathematica
Select[Range[500], PrimeQ[ #^2+#-1] && PrimeQ[ #^2+#+1] &] (* T. D. Noe, Jun 22 2004 *) Select[Range[1000],AllTrue[#^2+#+{1,-1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 12 2017 *)
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PARI
for(n=1,10^3,if(isprime(n^2+n-1)&&isprime(n^2+n+1),print1(n,", "))) \\ Derek Orr, Dec 24 2015
Extensions
Corrected description from T. D. Noe, Jun 22 2004
Comments