OFFSET
1,2
COMMENTS
Löschian numbers are numbers of the form x^2 + xy + y^2 for integers x, y; they can all be written in the form 4^e * m where e is a nonnegative integer and m is an odd Löschian number. - Charles R Greathouse IV, Jan 04 2016
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Joerg Arndt, Plane-filling curves on all uniform grids, arXiv preprint arXiv:1607.02433 [math.CO], 2016.
MATHEMATICA
fQ[n_] := Resolve[Exists[{x, y}, Reduce[n == x^2 + x y + y^2, {x, y}, Integers]]]; Select[2 Range@ 155 - 1, fQ] (* Michael De Vlieger, Jan 04 2016, after Jean-François Alcover at A003136 *)
PROG
(PARI) is(n)=(n%2==1) && #bnfisintnorm(bnfinit(z^2+z+1), n);
(PARI) x='x+O('x^1000); p=eta(x)^3/eta(x^3); for(n=0, 999, if(polcoeff(p, n) != 0 && n%2==1, print1(n, ", "))) \\ Altug Alkan, Jan 04 2016
(PARI) list(lim)=my(v=List(), y, t); for(x=0, sqrtint(lim\3), my(y=x, t); while((t=x^2+x*y+y^2)<=lim, if(t%2, listput(v, t)); y++)); Set(v) \\ Charles R Greathouse IV, Jul 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Jan 04 2016
STATUS
approved