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

1,1

Comments

Intersection of A239115 and A239135.

Links

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

Example

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.

Prog

(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;

Crossrefs

Sequence in context: A364606 A244790 A111503 * A075530 A032061 A350435

Adjacent sequences: A239323 A239324 A239325 * A239327 A239328 A239329

Keyword

nonn,easy

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Mar 16 2014

Extensions

Edited by Alois P. Heinz, Mar 19 2014

Status

approved