A239326 Numbers k such that k^2 +/- (k-1) and (k-1)*k^2 +/- 1 are all primes.

2, 3, 6, 13, 21, 100, 120, 195, 393, 541, 1749, 1849, 3640, 3829, 4003, 5488, 5754, 8973, 8989, 9043, 10824, 10828, 13488, 17016, 18493, 19306, 21505, 24270, 27139, 30163, 31530, 34134, 35034, 39514, 40761, 46215, 46285, 46398, 49071, 49869, 53319, 55320

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 16 2014

Keywords

• nonn
• easy

Comments

Intersection of A239115 and A239135.

Examples

			6 is this sequence because (6-1)*6^2-1 = 179, (6-1)*6^2+1 = 181, 6^2-6+1 = 31 and 6^2+6-1 = 41 are all primes.
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Programs

Magma

k := 1;
     for n in [1..100000] do
        if IsPrime(k*(n - 1)*n^2 + 1) and IsPrime(k*(n - 1)*n^2 - 1) and IsPrime(k*n^2 + n - 1) and IsPrime(k*n^2 - n + 1) then
           n;
        end if;
     end for;

Extensions

Edited by Alois P. Heinz, Mar 19 2014