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

%I A108768 #17 Dec 18 2017 03:00:44
%S A108768 3,7,13,7,31,43,19,73,13,37,19,157,61,211,241,307,127,421,463,79,601,
%T A108768 31,37,757,271,67,331,151,1123,397,97,43,67,1483,223,547,1723,139,631,
%U A108768 283,109,103,61,181,2551,379,919,409,2971,79,103,3307,163,3541,523,97,3907
%N A108768 Primes that appear in the sequence p:=x^2+x+1, sieved with a quadratic sieve construction.
%C A108768 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
%H A108768 Bernhard Helmes, <a href="http://www.devalco.de/quadr_Sieb_x%5E2+x+1.php">Prime sieving on the polynomial f(n)=n^2+n+1</a>.
%H A108768 Bernhard Helmes, <a href="http://web.archive.org/web/20050407001733/http://www.devalco.de/quadratisches_Siebverfahren.htm">Quadratic Sieve Construction</a> (web.archive).
%o A108768 (MuPAD) // from Quadratic Sieve Construction link.
%o A108768 liste_max:=10000;
%o A108768 for x from 1 to liste_max do
%o A108768     liste_x[x]:=x^2+x+1;
%o A108768     liste_prim[x]:=1;
%o A108768 end_for;
%o A108768 x:=1;
%o A108768 while (x<liste_max) do
%o A108768    stelle:=x;
%o A108768    p:=liste_x[x];
%o A108768    if (p>1) then
%o A108768      print ("Prim ", p, "x = ", x, isprime (p)) ;
%o A108768      // Aussiebung
%o A108768      while (stelle<liste_max) do
%o A108768         erg:=liste_x[stelle];
%o A108768         while (erg mod p = 0) do
%o A108768            erg:=erg /p;
%o A108768         end_while;
%o A108768         liste_x[stelle]:=erg;
%o A108768         liste_prim[stelle]:=0;
%o A108768         // print ("x= ",stelle, erg, p);
%o A108768         stelle:=stelle+p;
%o A108768      end_while;
%o A108768    end_if;
%o A108768    x:=x+1;
%o A108768 end_while;
%o A108768 // _Ray Chandler_, Jul 05 2015
%Y A108768 Cf. A002061, A002383, A007645, A162471, A256148.
%K A108768 nonn,uned,obsc
%O A108768 1,1
%A A108768 Bernhard Helmes (pi(AT)devalco.de), Jun 24 2005