A030051 - OEIS

%I #33 Jan 13 2022 10:00:44

%S 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,

%T 110,145,203,290

%N Numbers from the 290-theorem.

%C 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

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

%H Manjul Bhargava and Jonathan Hanke, <a href="http://www.wordpress.jonhanke.com/wp-content/uploads/2011/09/290-Theorem-preprint.pdf">Universal quadratic forms and the 290-Theorem</a> Inventiones Math., 2005

%H Jangwon Ju and Byeong-Kweon Oh, <a href="https://arxiv.org/abs/1809.03673">Universal mixed sums of generalized 4- and 8-gonal numbers</a>, arXiv:1809.03673 [math.NT], 2018. See p. 1.

%H Alexander J. Hahn, <a href="https://math.nd.edu/assets/20630/hahntoulouse.pdf">Quadratic Forms over Z from Diophantus to the 290 Theorem</a>, Adv. Appl. Clifford Alg. 18 (2008), 665-676.

%H Jangwon Ju, <a href="https://arxiv.org/abs/2201.04355">Almost universal sums of triangular numbers with one exception</a>, arXiv:2201.04355 [math.NT], 2022.

%H Yong Suk Moon, <a href="https://web.archive.org/web/20140814082644/https://math.stanford.edu/theses/moon.pdf">Universal Quadratic Forms and the 15-Theorem and 290-Theorem</a>

%H K. Ono, <a href="http://www.ams.org/notices/200606/fea-ono.pdf">Honoring a gift from Kumbakonam</a>, Notices Amer. Math. Soc., 53 (2006), 640-651.

%H Ivars Peterson, <a href="http://www.sciencenews.org/articles/20060311/bob9.asp">All Square: Science News Online</a>

%H Ivars Peterson, MathTrek, <a href="http://blog.sciencenews.org/2006/03/all_square.html">All Square</a>

%Y Cf. A030050, A116582, A154363.

%K nonn,fini,full,nice

%O 1,2

%A _N. J. A. Sloane_