A096012 Numbers k such that k^2+1 and (k+2)^2+1 are both prime; twin k^2+1 primes.

2, 4, 14, 24, 54, 124, 204, 384, 464, 634, 644, 714, 1094, 1144, 1174, 1244, 1274, 1314, 1374, 1564, 1614, 1674, 1684, 1964, 2054, 2084, 2094, 2404, 2454, 2534, 2664, 2834, 2924, 3134, 3304, 3534, 3754, 3774, 4024, 4154, 4174, 4364, 4604, 4614, 4734, 4784

Offset: 1

Author

Jason Earls, Jul 20 2004

Keywords

• easy
• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Seiichi Manyama)

Crossrefs

Cf. A005574, A108814.

Programs

Magma

[n: n in [1..5000] | IsPrime(n^2+1) and IsPrime((n+2)^2+1)]; // Vincenzo Librandi, Feb 27 2016

Mathematica

Select[Range[5000],AllTrue[{#^2+1,(#+2)^2+1},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 23 2014 *)
Select[Range[5000], PrimeQ[#^2 + 1] && PrimeQ[(# + 2)^2 + 1] &] (* Vincenzo Librandi, Feb 27 2016 *)

PARI

isok(n) = isprime(n^2+1) && isprime((n+2)^2+1); \\ Michel Marcus, Feb 27 2016

Formula

a(k) = A108814(k) - 1. - Jeppe Stig Nielsen, Feb 26 2016