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A003585 Odd numbers that are not of the form x^2 + y^2 + 10*z^2. 2
3, 7, 21, 31, 33, 43, 67, 79, 87, 133, 217, 219, 223, 253, 307, 391, 679, 2719 (list; graph; refs; listen; history; text; internal format)
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]
REFERENCES
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
Cf. A002145.
Sequence in context: A090504 A018548 A323585 * A108102 A357898 A065523
KEYWORD
nonn,fini,full,nice
AUTHOR
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)