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A108768 Primes that appear in the sequence p:=x^2+x+1, sieved with a quadratic sieve construction. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 14 19:35 EST 2018. Contains 318106 sequences. (Running on oeis4.)