|
|
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
|
|
|
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
|
|
|
|