

A030051


Numbers from the 290theorem.


6



1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290
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OFFSET

1,2


COMMENTS

The 290theorem, conjectured by Conway and Schneeberger and proved by Bhargava and Hanke, asserts that a positive definite quadratic form represents all numbers iff it represents the numbers in this sequence.  T. D. Noe, Mar 30 2006


REFERENCES

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


LINKS

Table of n, a(n) for n=1..29.
Manjul Bhargava and Jonathan Hanke, Universal quadratic forms and the 290Theorem Inventiones Math., 2005
Jangwon Ju, ByeongKweon Oh, Universal mixed sums of generalized 4 and 8gonal numbers, arXiv:1809.03673 [math.NT], 2018. See p. 1.
Alexander J. Hahn, Quadratic Forms over Z from Diophantus to the 290 Theorem, Adv. Appl. Clifford Alg. 18 (2008), 665676.
Yong Suk Moon, Universal Quadratic Forms and the 15Theorem and 290Theorem
K. Ono, Honoring a gift from Kumbakonam, Notices Amer. Math. Soc., 53 (2006), 640651.
Ivars Peterson, All Square: Science News Online
Ivars Peterson, MathTrek, All Square


CROSSREFS

Cf. A030050, A116582, A154363.
Sequence in context: A239746 A101323 A298705 * A344308 A183071 A139826
Adjacent sequences: A030048 A030049 A030050 * A030052 A030053 A030054


KEYWORD

nonn,fini,full,nice


AUTHOR

N. J. A. Sloane


STATUS

approved



