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A030051 Numbers from the 290-theorem. 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 (list; graph; refs; listen; history; text; internal format)



The 290-theorem, 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


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


Table of n, a(n) for n=1..29.

Manjul Bhargava and Jonathan Hanke, Universal quadratic forms and the 290-Theorem Inventiones Math., 2005

Jangwon Ju, Byeong-Kweon Oh, Universal mixed sums of generalized 4- and 8-gonal 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), 665-676.

Yong Suk Moon, Universal Quadratic Forms and the 15-Theorem and 290-Theorem

K. Ono, Honoring a gift from Kumbakonam, Notices Amer. Math. Soc., 53 (2006), 640-651.

Ivars Peterson, All Square: Science News Online

Ivars Peterson, MathTrek, All Square


Cf. A030050, A116582, A154363.

Sequence in context: A239746 A101323 A298705 * A344308 A183071 A139826

Adjacent sequences:  A030048 A030049 A030050 * A030052 A030053 A030054




N. J. A. Sloane



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Last modified November 30 04:10 EST 2021. Contains 349417 sequences. (Running on oeis4.)