A108768 Primes that appear in the sequence p:=x^2+x+1, sieved with a quadratic sieve construction.

3, 7, 13, 7, 31, 43, 19, 73, 13, 37, 19, 157, 61, 211, 241, 307, 127, 421, 463, 79, 601, 31, 37, 757, 271, 67, 331, 151, 1123, 397, 97, 43, 67, 1483, 223, 547, 1723, 139, 631, 283, 109, 103, 61, 181, 2551, 379, 919, 409, 2971, 79, 103, 3307, 163, 3541, 523, 97, 3907

Offset

1,1

Comments

This sequence appears in a website available on web.archive (see Quadratic Sieve Construction link). There is a single appearance of the first term 3, while all other primes appear twice. See A256148 for a version of the sequence consistent with the current version of the website where each prime appears only once. - Ray Chandler, Jul 05 2015

Links

Table of n, a(n) for n=1..57.

Bernhard Helmes, Prime sieving on the polynomial f(n)=n^2+n+1.

Bernhard Helmes, Quadratic Sieve Construction (web.archive).

Prog

(MuPAD) // from Quadratic Sieve Construction link.
liste_max:=10000;
for x from 1 to liste_max do
    liste_x[x]:=x^2+x+1;
    liste_prim[x]:=1;
end_for;
x:=1;
while (x<liste_max) do
   stelle:=x;
   p:=liste_x[x];
   if (p>1) then
     print ("Prim ", p, "x = ", x, isprime (p)) ;
     // Aussiebung
     while (stelle<liste_max) do
        erg:=liste_x[stelle];
        while (erg mod p = 0) do
           erg:=erg /p;
        end_while;
        liste_x[stelle]:=erg;
        liste_prim[stelle]:=0;
        // print ("x= ", stelle, erg, p);
        stelle:=stelle+p;
     end_while;
   end_if;
   x:=x+1;
end_while;
// Ray Chandler, Jul 05 2015

Crossrefs

Cf. A002061, A002383, A007645, A162471, A256148.

Sequence in context: A258136 A209387 A128156 * A238476 A118889 A077149

Adjacent sequences: A108765 A108766 A108767 * A108769 A108770 A108771

Keyword

nonn,uned,obsc

Author

Bernhard Helmes (pi(AT)devalco.de), Jun 24 2005

Status

approved