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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 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 A065523 A046528 Adjacent sequences:  A003582 A003583 A003584 * A003586 A003587 A003588 KEYWORD nonn,fini,full,nice AUTHOR STATUS approved

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Last modified June 23 08:25 EDT 2021. Contains 345395 sequences. (Running on oeis4.)