cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A028954 Numbers represented by quadratic form with Gram matrix [ 2, 1; 1, 6 ]. (divided by 2).

Original entry on oeis.org

0, 1, 3, 4, 5, 9, 11, 12, 15, 16, 20, 23, 25, 27, 31, 33, 36, 37, 44, 45, 47, 48, 49, 53, 55, 59, 60, 64, 67, 69, 71, 75, 80, 81, 89, 92, 93, 97, 99, 100, 103, 108, 111, 113, 115, 121, 124, 125, 132, 135, 137, 141, 144, 147, 148, 155, 157, 159, 163, 165, 169, 176, 177
Offset: 1

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Author

N. J. A. Sloane

Keywords

Comments

Numbers represented by the form x^2+xy+3y^2 of discriminant -11.

Links

Crossrefs

Cf. A028927. For primes see A056874.

Programs

  • Mathematica
    Reap[For[n = 0, n < 200, n++, r = Reduce[x^2 + x y + 3 y^2 == n, {x, y}, Integers]; If[r =!= False, Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 31 2016 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 29 2000

A028955 Numbers represented by quadratic form with Gram matrix [ 4, 1; 1, 4 ] (divided by 2).

Original entry on oeis.org

0, 2, 3, 5, 8, 12, 17, 18, 20, 23, 27, 30, 32, 38, 45, 47, 48, 50, 53, 57, 62, 68, 72, 75, 80, 83, 92, 93, 95, 98, 102, 107, 108, 113, 120, 122, 125, 128, 137, 138, 147, 152, 153, 155, 158, 162, 167, 170, 173, 180, 183, 188, 192, 197, 200, 207, 212, 218, 227, 228
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Numbers of the form 2*x^2 + x*y + 2*y^2, of discriminant -15. - N. J. A. Sloane, Jun 01 2014
8*a(n) is of the form z^2 + 15*y^2, where z = 4*x + y. [Bruno Berselli, Jul 12 2014]

Examples

			32 is in the sequence because it can be written in the form 2*2^2+2*3+2*3^2, and hence 8*32 = 11^2+15*3^2.

Links

Crossrefs

Cf. A028927. For primes see A106859.

Formula

a(x, y) = (4x^2 + 2xy + 4y^2)/2; x, y any integer.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 29 2000

A029718 Numbers of form 2x^2 + 2xy + 3y^2.

Original entry on oeis.org

0, 2, 3, 7, 8, 10, 12, 15, 18, 23, 27, 28, 32, 35, 40, 42, 43, 47, 48, 50, 58, 60, 63, 67, 72, 75, 82, 83, 87, 90, 92, 98, 103, 107, 108, 112, 115, 122, 123, 127, 128, 135, 138, 140, 147, 160, 162, 163, 167, 168, 172, 175, 178, 183, 188, 192, 200, 202, 203, 207, 210
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Numbers represented by quadratic form with Gram matrix [ 2, 1; 1, 3 ].

References

  • H. Cohn, A second course in number theory, John Wiley & Sons, Inc., New York-London, 1962. see page 3.

Links

Crossrefs

Cf. A028927.
For primes see A106865.
For the properly represented numbers see A344232.

Formula

List contains 0 and all positive n such that 2*A035170(n) = A028586(n) is nonzero. - Michael Somos, Oct 21 2006

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 29 2000
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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