OFFSET
1,2
COMMENTS
For these k, there exist an integer m such that quintic trinomial x^5-k*x+m is reducible into cubic and quadratic factors.
Negative numbers of the form -d^4 + 3 d^2 e - e^2.
The curve is equivalent to Y^2 = 5*X^3 + 4k*X, where Y=xy and X=x^2. - Max Alekseyev, Apr 26 2015
FORMULA
Complement to A193528
MATHEMATICA
aa = {}; Do[Do[k = -d^4 + 3 d^2 e - e^2; If[-k > 0, AppendTo[aa, -k ]], {d, -100, 100}], {e, -100, 100}]; Take[Union[aa], 100]
PROG
(Magma) for k:=1 to 1000 do if IntegralQuarticPoints([5, 0, 0, 0, 4*k]) ne [] then print(k); end if; end for; /* Max Alekseyev, Apr 26 2015 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jul 31 2011
EXTENSIONS
Terms a(32) onward from Max Alekseyev, Apr 26 2015
STATUS
approved