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.

A123068 Numbers represented by the "Little Methuselah" quadratic form x^2 + 2*y^2 + y*z + 4*z^2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75
Offset: 1

Views

Author

N. J. A. Sloane, Sep 27 2006

Keywords

Comments

Theorem (Conway, p. 81) This ternary form represents every number from 0 to 32 except 31. Any other integer-valued ternary form not equivalent to this one fails to represent some number between 1 and 30.

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, p. 82.

Crossrefs

Cf. A123063, A123064, A123065, A123067.

Programs

  • Magma
    L:=LatticeWithGram(3, [2,0,0,0,4,1,0,1,8] ); T := ThetaSeries(L,500); T;
Showing 1-3 of 3 results.

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

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