A260682 Löschian numbers (A003136) of the form 6*k+1.

1, 7, 13, 19, 25, 31, 37, 43, 49, 61, 67, 73, 79, 91, 97, 103, 109, 121, 127, 133, 139, 151, 157, 163, 169, 175, 181, 193, 199, 211, 217, 223, 229, 241, 247, 259, 271, 277, 283, 289, 301, 307, 313, 325, 331, 337, 343, 349, 361, 367, 373, 379, 397, 403, 409, 421, 427, 433, 439, 457, 463, 469, 475, 481, 487, 499

Offset: 1

Author

Joerg Arndt, Nov 15 2015

Keywords

• nonn

Comments

Odd terms of A202822, which lists Löschian numbers of the form 3*k+1. - Altug Alkan, Nov 15 2015

Links

• Reinhard Zumkeller, 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.

Crossrefs

Cf. A003136, A016921, A202822.

Programs

Haskell

a260682 n = a260682_list !! (n-1)
a260682_list = filter ((== 1) . flip mod 6) a003136_list
-- Reinhard Zumkeller, Nov 16 2015

Mathematica

nn = 25; Select[Union[Flatten[Table[x^2 + x*y + y^2, {x, 0, nn}, {y, 0, x}]]], Mod[#, 6] == 1 && # <= nn^2&] (* Jean-François Alcover, Jul 21 2018, after T. D. Noe *)

PARI

is(n)=(n%6==1)&&#bnfisintnorm(bnfinit(z^2+z+1), n);
select(n->is(n), vector(500,j,j))

PARI

x='x+O('x^500); p=eta(x)^3/eta(x^3); for(n=0, 499, if(polcoeff(p, n) != 0 && n%6==1, print1(n, ", "))) \\ Altug Alkan, Nov 15 2015

PARI

isok(n) = if( n<1 || (n%3 == 0), 0, 0 != sumdiv( n, d, kronecker( -3, d))) && n%2==1;
for(n=0, 500, if(isok(n), print1(n", "))) \\ Altug Alkan, Nov 15 2015

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%6==1, listput(v, t)); y++)); Set(v) \\ Charles R Greathouse IV, Jul 05 2017