A266836 Odd Löschian numbers.

1, 3, 7, 9, 13, 19, 21, 25, 27, 31, 37, 39, 43, 49, 57, 61, 63, 67, 73, 75, 79, 81, 91, 93, 97, 103, 109, 111, 117, 121, 127, 129, 133, 139, 147, 151, 157, 163, 169, 171, 175, 181, 183, 189, 193, 199, 201, 211, 217, 219, 223, 225, 229, 237, 241, 243, 247, 259, 271, 273, 277, 279, 283, 289, 291, 301, 307, 309

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

Cf. Loeschian numbers: A003136 (all), A202822 (3*k+1), A260682 (6*k+1).

Sequence in context: A089556 A225495 A111223 * A066207 A141544 A172407

Adjacent sequences: A266833 A266834 A266835 * A266837 A266838 A266839

Keyword

nonn

Author

Joerg Arndt, Jan 04 2016

Status

approved