A393168 - OEIS

%I #31 Feb 10 2026 20:42:22

%S 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,

%T 31,32,33,34,36,37,39,40,41,43,44,45,46,47,48,49,50,51,52,53,54,56,57,

%U 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

%N 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.

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

%H Emmanuel Osalotioman Osazuwa, <a href="/A393168/b393168.txt">Table of n, a(n) for n = 1..10000</a>

%H Thomas Bloom, <a href="https://www.erdosproblems.com/1148">Problem 1148</a>, Erdős Problems.

%o (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))

%Y Cf. A390380 (complement).

%K nonn

%O 1,3

%A _Emmanuel Osalotioman Osazuwa_, Feb 04 2026