A393168 Integers k which can be written in the form x^2 + y^2 - z^2, where x, y, z are integers and x^2, y^2, z^2 <= k.

0, 1, 2, 4, 5, 7, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 84, 85, 86

Offset

1,3

Comments

It is conjectured that every number greater than 6563 can be written in this form.

Links

Emmanuel Osalotioman Osazuwa, Table of n, a(n) for n = 1..10000

Thomas Bloom, Problem 1148, Erdős Problems.

Prog

(Python) isok = lambda k, math=__import__('math'): any(any(0 <= (k + z**2 - x**2) <= k and math.isqrt(k + z**2 - x**2)**2 == (k + z**2 - x**2) for x in range(math.isqrt(k) + 1)) for z in range(math.isqrt(k) + 1))

Crossrefs

Cf. A390380 (complement).

Sequence in context: A235331 A175969 A183573 * A187895 A079726 A047498

Adjacent sequences: A393165 A393166 A393167 * A393169 A393170 A393171

Keyword

nonn

Author

Emmanuel Osalotioman Osazuwa, Feb 04 2026

Status

approved