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

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Example

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

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, 369}] // Flatten

Prog

(Python)
from math import isqrt
def aupto(limit):
  m = isqrt(limit) + 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

Crossrefs

Cf. A000404, A010052, A057653, A097269.

Cf. A016742, A016754.

Sequence in context: A105596 A037046 A126887 * A087445 A380657 A020882

Adjacent sequences: A339949 A339950 A339951 * A339953 A339954 A339955

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 24 2020

Status

approved