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A192511 Number of conjugacy classes of primitive elements in GF(13^n) which have trace 0. 6
0, 0, 18, 112, 1904, 17184 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also number of primitive polynomials of degree n over GF(13) whose second-highest coefficient is 0.

LINKS

Table of n, a(n) for n=1..6.

FORMULA

a(n) = A192216(n) / n.

PROG

(GAP)

p := 13;

a := function(n)

    local q, k, cnt, x;

    q:=p^n;  k:=GF(p, n);  cnt:=0;

    for x in k do

        if Trace(k, GF(p), x)=0*Z(p) and Order(x)=q-1 then

            cnt := cnt+1;

        fi;

    od;

    return cnt/n;

end;

for n in [1..16] do  Print (a(n), ", ");  od;

(Sage) # See A192507 (change first line p=3 to p=13)

CROSSREFS

Cf. A152049 (GF(2^n)), A192507 (GF(3^n)), A192508 (GF(5^n)), A192509 (GF(7^n)), A192510 (GF(11^n)).

Sequence in context: A213562 A041622 A160765 * A324623 A244866 A125328

Adjacent sequences:  A192508 A192509 A192510 * A192512 A192513 A192514

KEYWORD

nonn,hard,more

AUTHOR

Joerg Arndt, Jul 03 2011

STATUS

approved

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Last modified May 26 09:52 EDT 2019. Contains 323579 sequences. (Running on oeis4.)