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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

Table of n, a(n) for n=1..18.

Ben Kane, Representing Sets With Sums Of Triangular Numbers

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-Fran├žois 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

N. J. A. Sloane

STATUS

approved

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Last modified January 24 10:33 EST 2020. Contains 331193 sequences. (Running on oeis4.)