A260682 - OEIS

%I #35 Jul 21 2018 08:28:31

%S 1,7,13,19,25,31,37,43,49,61,67,73,79,91,97,103,109,121,127,133,139,

%T 151,157,163,169,175,181,193,199,211,217,223,229,241,247,259,271,277,

%U 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

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

%C Odd terms of A202822, which lists Löschian numbers of the form 3*k+1. - _Altug Alkan_, Nov 15 2015

%H Reinhard Zumkeller, <a href="/A260682/b260682.txt">Table of n, a(n) for n = 1..10000</a>

%H Joerg Arndt, <a href="https://arxiv.org/abs/1607.02433">Plane-filling curves on all uniform grids</a>, arXiv preprint arXiv:1607.02433 [math.CO], 2016.

%t 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_ *)

%o (PARI) is(n)=(n%6==1)&&#bnfisintnorm(bnfinit(z^2+z+1), n);

%o select(n->is(n), vector(500,j,j))

%o (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

%o (PARI) isok(n) = if( n<1 || (n%3 == 0), 0, 0 != sumdiv( n, d, kronecker( -3, d))) && n%2==1;

%o for(n=0, 500, if(isok(n), print1(n", "))) \\ _Altug Alkan_, Nov 15 2015

%o (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

%o (Haskell)

%o a260682 n = a260682_list !! (n-1)

%o a260682_list = filter ((== 1) . flip mod 6) a003136_list

%o -- _Reinhard Zumkeller_, Nov 16 2015

%Y Cf. A003136, A016921, A202822.

%K nonn

%O 1,2

%A _Joerg Arndt_, Nov 15 2015