A239115 Numbers n such that (n-1)*n^2-1 and n^2-(n-1) are both prime.

2, 3, 4, 6, 7, 9, 13, 18, 21, 22, 58, 67, 79, 90, 100, 106, 111, 118, 120, 144, 162, 174, 195, 204, 246, 273, 279, 345, 393, 403, 406, 435, 436, 526, 541, 567, 613, 625, 636, 702, 721, 729, 736, 744, 762, 763, 865, 898, 961, 970, 993, 1059, 1099, 1117, 1131

Offset

1,1

Comments

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

Intersection of A162293 and A055494.

Primes in this sequence: 2, 3, 7, 13, 67, 79, 541, 613, 1117, ...

Squares in this sequence: 4, 9, 100, 144, 961, ...

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Example

13 is in this sequence because (13-1)*13^2-1 = 2027 and 13^2-(13-1) = 157 are both prime.

Mathematica

Select[Range[1000], PrimeQ[#^3 - #^2 - 1] && PrimeQ[#^2 - # + 1] &] (* Giovanni Resta, Mar 10 2014 *)
Select[Range[1200], PrimeOmega[#^5-2#^4+2#^3-2#^2+#-1]==2&] (* Harvey P. Dale, Sep 24 2014 *)

Prog

(PARI) isok(n) = isprime(n^3-n^2-1) && isprime(n^2-n+1); \\ Michel Marcus, Mar 10 2014
(Magma) k:=1;
    for n in [1..1000] do
     if IsPrime(k*(n-1)*n^2-1) and IsPrime(k*n^2-n+1) then
            n;
      end if;
    end for;  \\ Juri-Stepan Gerasimov, Mar 18 2014

Crossrefs

Cf. A162291, A002383, A239135, A239326.

Sequence in context: A161890 A089388 A055494 * A165773 A064414 A224482

Adjacent sequences: A239112 A239113 A239114 * A239116 A239117 A239118

Keyword

nonn

Author

Ilya Lopatin following a suggestion from Juri-Stepan Gerasimov, Mar 10 2014,

Extensions

More terms from Giovanni Resta, Mar 10 2014

Status

approved