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A202822 Numbers of the form 3*(x^2 + xy + y^2 + x + y) + 1 where x and y are integers. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Closed under multiplication.
Löschian numbers of the form 3*k+1. - Altug Alkan, Nov 18 2015
LINKS
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
Subsequence of A003136, A260682 (subsequence).
Sequence in context: A230745 A191201 A084089 * A137827 A045090 A213382
KEYWORD
nonn
AUTHOR
Michael Somos, Dec 25 2011
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)