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.

A123064 Numbers represented by the quadratic form 2 x^2 + xy + 4 y^2.

Original entry on oeis.org

0, 2, 4, 5, 7, 8, 10, 14, 16, 18, 19, 20, 25, 28, 32, 35, 36, 38, 40, 41, 45, 49, 50, 56, 59, 62, 63, 64, 70, 71, 72, 76, 80, 82, 90, 94, 95, 97, 98, 100, 101, 103, 107, 109, 112, 113, 118, 124, 125, 126, 128, 133, 134, 140, 142, 144, 152, 155, 157, 160, 162, 163, 164, 171, 175
Offset: 1

Views

Author

N. J. A. Sloane, Sep 27 2006

Keywords

References

  • J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 82.

Links

Crossrefs

Cf. A123063, A123065, A123067, A123068.
Primes: A106872.

Programs

  • Magma
    L:=LatticeWithGram(2, [4,1,1,8] ); T := ThetaSeries(L,500); T;

A123065 Numbers primitively represented by the quadratic form 2 x^2 + xy + 4 y^2.

Original entry on oeis.org

2, 4, 5, 7, 10, 14, 16, 19, 20, 25, 28, 32
Offset: 1

Views

Author

N. J. A. Sloane, Sep 27 2006

Keywords

References

  • J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 82.

Crossrefs

Cf. A123063, A123064, A123067, A123068.

A123067 Theta series of the "Little Methuselah" quadratic form x^2 + 2*y^2 + y*z + 4*z^2.

Original entry on oeis.org

1, 2, 2, 4, 4, 6, 8, 2, 10, 10, 2, 12, 4, 4, 10, 4, 10, 12, 10, 10, 20, 12, 4, 12, 12, 12, 8, 8, 8, 24, 8, 0, 24, 12, 8, 10, 24, 12, 6, 12, 14, 38, 8, 8, 32, 18, 8, 4, 8, 20, 20, 16, 12, 16, 24, 4, 30, 28, 4, 14, 20, 12, 2, 18, 18, 44, 20, 8, 28, 12, 10, 26, 30, 12, 28, 16, 20, 20, 8, 16, 34
Offset: 0

Views

Author

N. J. A. Sloane, Sep 27 2006, corrected Oct 26 2006

Keywords

Comments

The Little Methuselah form represents every integer from 1 to 30, but fails to represent 31. Every integer-valued positive definite ternary form not equivalent to it fails to represent some integer between 1 and 30. [Conway]

Examples

			1 + 2*x + 2*x^2 + 4*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 2*x^7 + 10*x^8 + 10*x^9 + 2*x^10 + ...

References

  • J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, pp. 81-82.

Crossrefs

Cf. A123063, A123064, A123065, A123068.

Programs

  • Magma
    L:=LatticeWithGram(3, [2,0,0,0,4,1,0,1,8] ); T := ThetaSeries(L,500); T;
  • PARI
    {a(n)= if(n<1, n==0, qfrep([2, 0, 0; 0, 4, 1; 0, 1, 8],n, 1)[n]*2)} /* Michael Somos, Oct 23 2006 */
Showing 1-3 of 3 results.

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

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