A242665 Nonnegative integers of the form -x^2 + 4xy + 2y^2.

0, 2, 5, 6, 8, 15, 18, 20, 23, 24, 29, 32, 38, 45, 47, 50, 53, 54, 60, 69, 71, 72, 80, 86, 87, 92, 95, 96, 98, 101, 114, 116, 125, 128, 134, 135, 141, 146, 149, 150, 152, 159, 162, 167, 173, 180, 188, 191, 194, 197, 200, 207, 212, 213, 215, 216, 230, 239, 240, 242, 245, 258, 261, 263, 269, 276, 278, 284, 285, 288, 290, 293, 294

Offset

1,2

Comments

Discriminant 24.

Multiplied by -1, these are the nonpositive norms of numbers in Z[sqrt(6)]. - Alonso del Arte, Sep 26 2014

Nonnegative integers of the form 2*x^2 - 3*y^2. - Robert Israel, Jun 03 2018

Nonnegative integers of the form 6*x^2 - y^2. - Jon E. Schoenfield, Jun 03 2022

Links

Robert Israel, Table of n, a(n) for n = 1..10000

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Math Stackexchange, Can the integers n expressible as 2a^2-3b^2 be classified?

Maple

filter:= proc(n) local F;
  F:= map(proc(t) local p; p:= t[1] mod 24; if t[2]::even or member(p, {3, 1, 19}) then NULL else p fi end proc, ifactors(n)[2]);
  if convert(F, set) intersect {7, 11, 13, 17} <> {} then return false fi;
  nops(F)::odd
end proc:
filter(0):= true:
select(filter, [$0..400]); # Robert Israel, Jun 03 2018

Mathematica

Reap[For[n = 0, n <= 300, n++, If[Reduce[-x^2 + 4*x*y + 2*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]]

Crossrefs

Primes in this sequence = A141171.

Sequence in context: A019989 A045547 A127143 * A079256 A191204 A191140

Adjacent sequences: A242662 A242663 A242664 * A242666 A242667 A242668

Keyword

nonn

Author

N. J. A. Sloane, May 31 2014

Status

approved