A339952 Numbers that are the sum of an even square > 0 and an odd square.

5, 13, 17, 25, 29, 37, 41, 45, 53, 61, 65, 73, 85, 89, 97, 101, 109, 113, 117, 125, 137, 145, 149, 153, 157, 169, 173, 181, 185, 193, 197, 205, 221, 225, 229, 233, 241, 245, 257, 261, 265, 269, 277, 281, 289, 293, 305, 313, 317, 325, 333, 337, 349, 353, 365, 369, 373, 377

Offset: 1

Author

Wesley Ivan Hurt, Dec 24 2020

Keywords

• nonn
• easy

Examples

			13 is in the sequence since it is the sum of an even square > 0 and an odd square, 2^2 + 3^2 = 4 + 9 = 13.
		

Crossrefs

Cf. A000404, A010052, A057653, A097269.

Programs

Mathematica

Table[If[Sum[Sign[(Mod[i, 2] Mod[n - i + 1, 2] + Mod[i + 1, 2] Mod[n - i, 2])] (Floor[Sqrt[i]] - Floor[Sqrt[i - 1]]) (Floor[Sqrt[n - i]] - Floor[Sqrt[n - i - 1]]), {i, Floor[n/2]}] > 0, n, {}], {n, 500}] // Flatten

Python

def aupto(limit):
  m = int(limit**.5) + 2
  es = [i*i for i in range(2, m, 2)]
  os = [i*i for i in range(1, m, 2)]
  return sorted(set(a+b for a in es for b in os if a+b <= limit))
print(aupto(377)) # Michael S. Branicky, May 13 2021