A390380 Integers k which cannot 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.

3, 6, 11, 15, 22, 27, 35, 38, 42, 55, 59, 66, 78, 83, 87, 95, 110, 118, 123, 131, 143, 150, 187, 210, 222, 227, 255, 262, 266, 278, 299, 303, 323, 326, 395, 402, 447, 483, 502, 551, 563, 590, 618, 635, 678, 735, 755, 838, 843, 867, 902, 930, 942, 1003, 1007, 1034, 1091, 1162, 1190

Offset

1,1

Comments

6563 is conjectured to be the largest integer of the sequence. All negative integers are also part of this sequence since the condition x^2, y^2, z^2 <= k will always fail for negative k, as x^2 >= 0.

Links

Emmanuel Osalotioman Osazuwa, Table of n, a(n) for n = 1..77

Thomas Bloom, Problem 1148, Erdős Problems.

Prog

(PARI) isok(k)=my(m=sqrtint(k)); if(m^2==k, 0, forstep(x=m, 0, -1, my(r=k-x^2); fordiv(r, d, my(y=(d+r/d)/2); if(!frac(y)&&y<=m, return(0)))); 1) \\ Andrew Howroyd, Feb 03 2026

Crossrefs

Cf. A393168 (complement).

Sequence in context: A324773 A373189 A152682 * A059753 A256001 A131665

Adjacent sequences: A390377 A390378 A390379 * A390381 A390382 A390383

Keyword

nonn

Author

Emmanuel Osalotioman Osazuwa, Jan 30 2026

Status

approved