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A030050 Numbers from the Conway-Schneeberger 15-theorem. 4
1, 2, 3, 5, 6, 7, 10, 14, 15 (list; graph; refs; listen; history; text; internal format)



The 15-theorem asserts that a positive definite integral quadratic form represents all numbers iff it represents the numbers in this sequence. "Integral" here means that the quadratic form equals x^T M x, where x is an integer vector and M is an integer matrix. - T. D. Noe, Mar 30 2006


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

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

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

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


Table of n, a(n) for n=1..9.

Manjul Bhargava, The Fifteen Theorem and Generalizations

Ivars Peterson, All Square: Science News Online (subscription required)


Cf. A030051, A116582, A154363.

Sequence in context: A139826 A182048 A028722 * A018336 A194359 A220355

Adjacent sequences:  A030047 A030048 A030049 * A030051 A030052 A030053




N. J. A. Sloane.



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Last modified December 19 07:22 EST 2014. Contains 252186 sequences.