A239135 Numbers k such that (k-1)*k^2 + 1 and k^2 + (k-1) are both prime.

2, 3, 5, 6, 8, 13, 21, 24, 26, 28, 35, 45, 48, 50, 55, 76, 83, 89, 93, 96, 100, 101, 115, 120, 138, 140, 148, 149, 181, 191, 195, 203, 206, 209, 215, 230, 258, 259, 281, 285, 294, 301, 309, 323, 330, 349, 358, 373, 380, 386, 393, 395, 423, 428, 433, 474, 495

Offset

1,1

Comments

Numbers k such that (k^3 - k^2 + 1)*(k^2 + k - 1) is semiprime.

Intersection of A045546 and A111501.

Primes in this sequence: 2, 3, 5, 13, 83, 89, 101, 149, 181, 191, ...

Links

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

Example

2 is in this sequence because (2-1)*2^2+1=5 and 2^2+(2-1)=5 are both prime.

Mathematica

Select[Range[600], PrimeQ[#^2+#-1]&&PrimeQ[#^2(#-1)+1]&] (* Farideh Firoozbakht, Mar 17 2014 *)

Prog

(Magma) k := 1;
     for n in [1..10000] do
        if IsPrime(k*(n - 1)*n^2 + 1) and IsPrime(k*n^2 + n - 1) then
           n;
        end if;
     end for;

Crossrefs

Cf. A239115.

Sequence in context: A034722 A144712 A050028 * A179791 A139443 A239263

Adjacent sequences: A239132 A239133 A239134 * A239136 A239137 A239138

Keyword

nonn

Author

Ilya Lopatin following a suggestion from Juri-Stepan Gerasimov, Mar 15 2014

Status

approved