OFFSET
1,1
COMMENTS
Under GRH the terms shown are the complete sequence.
The prime numbers in this sequence (3,7,31,43,67,79,223,307,2719) are of the form 4n+3. - Paul Muljadi, Jan 28 2011
Duke & Schulze-Pillot showed that this sequence is finite. - Charles R Greathouse IV, Jul 12 2024
REFERENCES
William Duke and Rainer Schulze-Pillot, Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids, Inventiones mathematicae, Volume 99, pages 49-57, (1990).
K. Ono, Ramanujan's ternary quadratic form, Abstract 914-11-96, Abstracts Amer. Math. Soc., 17 (1996), 476.
Ken Ono and Amir D. Aczel, "My search for Ramanujan", Springer, 2016; see p. 182, lines 12 and 11 from the bottom. but there is an error.
S. Ramanujan, Coll. Papers, p. 172.
LINKS
Amir Jafari and Farhood Rostamkhani, On ternary quadratic forms over the rational numbers, arXiv:2109.10225 [math.HO], 2021. See p. 3.
Ben Kane, Representing Sets With Sums Of Triangular Numbers, Int. Math. Res. Not., Vol. 2009, No. 17, pp. 3264-3285, arXiv:0903.3026 [math.NT], 2009.
K. Ono, Ramanujan, taxicabs, birthdates, ZIP codes and twists, Amer. Math. Monthly, 104 (1997), 912-917.
K. Ono, Honoring a gift from Kumbakonam, Notices Amer. Math. Soc., 53 (2006), 640-651.
MATHEMATICA
r[n_, z_] := Reduce[n == x^2 + y^2 + 10*z^2, {x, y}, Integers]; A003585 = Reap[For[n=1, n<3000, n = n+2, If[Union[Table[r[n, z], {z, 0, Sqrt[n/10] // Ceiling}]] == {False}, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jul 06 2011, updated Jan 27 2015 *)
CROSSREFS
KEYWORD
nonn,fini,full,nice
AUTHOR
STATUS
approved