cp's OEIS Frontend

A192511 Number of conjugacy classes of primitive elements in GF(13^n) which have trace 0.

%I A192511 #15 Jun 02 2024 08:23:48
%S A192511 0,0,18,112,1904,17184,229848,1686008,29713758
%N A192511 Number of conjugacy classes of primitive elements in GF(13^n) which have trace 0.
%C A192511 Also number of primitive polynomials of degree n over GF(13) whose second-highest coefficient is 0.
%F A192511 a(n) = A192216(n) / n.
%o A192511 (GAP)
%o A192511 p := 13;
%o A192511 a := function(n)
%o A192511     local q, k, cnt, x;
%o A192511     q:=p^n;  k:=GF(p, n);  cnt:=0;
%o A192511     for x in k do
%o A192511         if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then
%o A192511             cnt := cnt+1;
%o A192511         fi;
%o A192511     od;
%o A192511     return cnt/n;
%o A192511 end;
%o A192511 for n in [1..16] do  Print (a(n), ", ");  od;
%o A192511 (Sage) # See A192507 (change first line p=3 to p=13)
%Y A192511 Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192508 (GF(5^n)), A192509 (GF(7^n)), A192510 (GF(11^n)).
%K A192511 nonn,hard,more
%O A192511 1,3
%A A192511 _Joerg Arndt_, Jul 03 2011
%E A192511 a(7)-a(9) from _Robin Visser_, Jun 01 2024