A030051 Numbers from the 290-theorem.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• fini
• full
• nice

Comments

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

References

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

Links

• Manjul Bhargava and Jonathan Hanke, Universal quadratic forms and the 290-Theorem Inventiones Math., 2005
• Jangwon Ju and 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.
• Jangwon Ju, Almost universal sums of triangular numbers with one exception, arXiv:2201.04355 [math.NT], 2022.
• 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

Crossrefs

Cf. A030050, A116582, A154363.