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

1,1

Comments

A265006 gives these primes. - Derek Orr, Dec 24 2015

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Example

20*20 + 20 - 1 = 419, 419 and 421 twin primes, 20 is the 7th of the sequence

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 *)

Prog

(PARI) for(n=1, 10^3, if(isprime(n^2+n-1)&&isprime(n^2+n+1), print1(n, ", "))) \\ Derek Orr, Dec 24 2015
(Magma) [n: n in [1..2*10^3] |IsPrime(n^2+n-1) and IsPrime(n^2+n+1)]; // Vincenzo Librandi, Dec 26 2015

Crossrefs

Cf. A088483, A265006.

Sequence in context: A239263 A216293 A088497 * A194626 A275323 A128994

Adjacent sequences: A088482 A088483 A088484 * A088486 A088487 A088488

Keyword

nonn,easy

Author

Pierre CAMI, Nov 09 2003

Extensions

Corrected description from T. D. Noe, Jun 22 2004

Status

approved