A139538 Odd numbers of the form x^2+5y^2 not divisible by 5, with both x and y >== 1.

9, 21, 29, 41, 49, 61, 69, 81, 89, 101, 109, 129, 141, 149, 161, 181, 189, 201, 229, 241, 249, 261, 269, 281, 301, 309, 321, 329, 349, 369, 381, 389, 401, 409, 421, 441, 449, 461, 469, 489, 501, 509, 521, 529, 541, 549, 569, 581, 601, 609, 621, 641, 661, 669

Offset: 1

Author

Artur Jasinski, Apr 25 2008, Apr 28 2008

Keywords

• nonn

Comments

All numbers in this sequence are divisible by primes A139513

References

• Dirichlet & Dedekins Lectures on Number Theory (English Translation 1999) p. 119.

Programs

Mathematica

a = {}; Do[Do[k = x^2 + 5 y^2; If[OddQ[k], If[Mod[k, 5] != 0, AppendTo[a, k]]], {x, 1, 100}], {y, 1, 100}]; Union[a] (*Artur Jasinski*)
With[{upto=1000},Select[Union[#[[1]]^2+5#[[2]]^2&/@Tuples[Range[Floor[ Sqrt[ upto-5]]],2]],OddQ[#]&&Mod[#,5]!=0&&#<=upto&]] (* Harvey P. Dale, Jul 25 2019 *)

Extensions

Definition clarified by Harvey P. Dale, Jul 25 2019