The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A198773 Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y. 8
49, 91, 133, 147, 169, 196, 217, 247, 259, 273, 301, 343, 361, 364, 399, 403, 427, 441, 469, 481, 507, 511, 532, 553, 559, 588, 589, 651, 676, 679, 703, 721, 741, 763, 777, 784, 793, 817, 819, 868, 871, 889, 903, 949, 961, 973, 988, 1027, 1029, 1036, 1057, 1083, 1092, 1099, 1141, 1147 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A088534(a(n)) = 2; subsequence of A118886, see also A003136.
LINKS
EXAMPLE
a(10) = 273 = 1^2 + 1*16 + 16^2 = 8^2 + 8*11 + 11^2, A088534(273) = 2;
a(11) = 301 = 4^2 + 4*15 + 15^2 = 9^2 + 9*11 + 11^2, A088534(301) = 2.
MATHEMATICA
amax = 2000; xmax = Sqrt[amax] // Ceiling; Clear[f]; f[_] = 0; Do[q = x^2 + x y + y^2; f[q] = f[q] + 1, {x, 0, xmax}, {y, x, xmax}];
A198773 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 2&] (* Jean-François Alcover, Jun 21 2018 *)
PROG
(Haskell)
a198773 n = a198773_list !! (n-1)
a198773_list = filter ((== 2) . a088534) a003136_list
(PARI) is(n)=my(t=#bnfisintnorm(bnfinit(z^2+z+1), n)); t==3 || t==4;
select(n->is(n), vector(1500, j, j)) \\ Joerg Arndt, Jan 11 2015
CROSSREFS
Sequence in context: A230226 A178705 A118886 * A320633 A108164 A020158
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 30 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 10:54 EDT 2024. Contains 372938 sequences. (Running on oeis4.)