A125018 Numbers == 1 (mod 4) with a unique partition as a sum of 2 squares x^2 + y^2.

1, 5, 9, 13, 17, 29, 37, 41, 45, 49, 53, 61, 73, 81, 89, 97, 101, 109, 113, 117, 121, 137, 149, 153, 157, 173, 181, 193, 197, 229, 233, 241, 245, 257, 261, 269, 277, 281, 293, 313, 317, 333, 337, 349, 353, 361, 369, 373, 389, 397, 401, 405, 409, 421, 433

Offset: 1

Author

Artur Jasinski, Nov 16 2006

Keywords

• nonn

Examples

			5 = 1^2 + 2^2, 9 = 0^2 + 3^2, 13 = 2^2 + 3^2, 17 = 1^2 + 4^2, 29 = 2^2 + 5^2, ... - _Michael Somos_, Jul 25 2023
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002145, A119345, A124982, A124983.

Programs

Mathematica

Select[4 * Range[0, 100] + 1, Length @ PowersRepresentations[#, 2, 2] == 1 &] (* Amiram Eldar, Mar 12 2020 *)

PARI

isok(n)= {if (n % 4 != 1, return(0)); A000161(n) == 1;} \\ Michel Marcus, Nov 02 2013

Extensions

More terms from Michel Marcus, Nov 02 2013