%I #19 Jul 29 2023 14:35:32

%S 1,5,9,13,17,29,37,41,45,49,53,61,73,81,89,97,101,109,113,117,121,137,

%T 149,153,157,173,181,193,197,229,233,241,245,257,261,269,277,281,293,

%U 313,317,333,337,349,353,361,369,373,389,397,401,405,409,421,433

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

%H Amiram Eldar, <a href="/A125018/b125018.txt">Table of n, a(n) for n = 1..10000</a>

%e 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

%t Select[4 * Range[0, 100] + 1, Length @ PowersRepresentations[#, 2, 2] == 1 &] (* _Amiram Eldar_, Mar 12 2020 *)

%o (PARI) isok(n)= {if (n % 4 != 1, return(0)); A000161(n) == 1;} \\ _Michel Marcus_, Nov 02 2013

%Y Cf. A002145, A119345, A124982, A124983.

%K nonn

%O 1,2

%A _Artur Jasinski_, Nov 16 2006

%E More terms from _Michel Marcus_, Nov 02 2013