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A266836 Odd Löschian numbers. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 20:17 EDT 2021. Contains 346294 sequences. (Running on oeis4.)