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A030050 Numbers from the Conway-Schneeberger 15-theorem. +0
3
1, 2, 3, 5, 6, 7, 10, 14, 15 (list; graph; listen)
OFFSET

1,2

COMMENT

The 15-theorem asserts that a positive definite integral quadratic form represents all numbers if it represents the numbers in this sequence. An integral quadratic form has the form x^T Mx, where x is an integer vector and M is an integer matrix. - T. D. Noe (noe(AT)sspectra.com), Mar 30 2006

REFERENCES

Manjul Bhargava, On the Conway-Schneeberger fifteen theorem, Contemporary Mathematics 272 (1999), 27-37.

J. H. Conway, Universal quadratic forms and the fifteen theorem, Contemporary Mathematics 272 (1999), 23-26.

J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 141.

J. H. Conway and W. A. Schneeberger, personal communication.

LINKS

Ivars Peterson, All Square: Science News Online

CROSSREFS

Cf. A030051, A116582.

Sequence in context: A030051 A139826 A028722 this_sequence A018336 A059041 A129128

Adjacent sequences: A030047 A030048 A030049 this_sequence A030051 A030052 A030053

KEYWORD

nonn,fini,full,nice

AUTHOR

njas

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Last modified July 25 02:12 EDT 2008. Contains 142294 sequences.


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