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

1,2

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.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A033685, A045833.

Subsequence of A003136, A260682 (subsequence).

Sequence in context: A230745 A191201 A084089 * A374135 A137827 A045090

Adjacent sequences: A202819 A202820 A202821 * A202823 A202824 A202825

Keyword

nonn

Author

Michael Somos, Dec 25 2011

Status

approved