A202822 Numbers of the form 3*(x^2 + xy + y^2 + x + y) + 1 where x and y are integers.

1, 4, 7, 13, 16, 19, 25, 28, 31, 37, 43, 49, 52, 61, 64, 67, 73, 76, 79, 91, 97, 100, 103, 109, 112, 121, 124, 127, 133, 139, 148, 151, 157, 163, 169, 172, 175, 181, 193, 196, 199, 208, 211, 217, 223, 229, 241, 244, 247, 256, 259, 268, 271, 277, 283, 289, 292

Offset: 1

Author

Michael Somos, Dec 25 2011

Keywords

• nonn

Comments

Closed under multiplication.

Löschian numbers of the form 3*k+1. - Altug Alkan, Nov 18 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. A033685, A045833.

Subsequence of A003136, A260682 (subsequence).

Programs

Haskell

a202822 n = a202822_list !! (n-1)
a202822_list = filter ((== 1) . flip mod 3) a003136_list
-- Reinhard Zumkeller, Nov 16 2015

Mathematica

nf[{i_,j_}]:=3(i^2+i*j+j^2+i+j)+1; Union[nf/@Tuples[Range[-10,10],2]] (* Harvey P. Dale, Dec 31 2011 *)

PARI

isA(n) = if(n%3 == 0, 0, 0 != sumdiv( n, d, kronecker( -3, d)))

PARI

x='x+O('x^500); p=eta(x)^3/eta(x^3); for(n=0, 499, if(polcoeff(p, n) != 0 && n%3==1, print1(n, ", "))) \\ Altug Alkan, Nov 18 2015

PARI

is(n)=(n%3==1) && #bnfisintnorm(bnfinit(z^2+z+1), n); \\ Joerg Arndt, 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((x-y)%3, listput(v, t)); y++)); Set(v) \\ Charles R Greathouse IV, Jul 05 2017

Formula

A033685(n) != 0 if and only if n is in the set.