A353219 Positive integers which cannot be expressed as the sum of three or fewer squares, no more than two of which are greater than 1.

7, 12, 15, 22, 23, 24, 28, 31, 39, 43, 44, 47, 48, 55, 56, 57, 60, 63, 67, 70, 71, 76, 77, 78, 79, 84, 87, 88, 92, 93, 94, 95, 96, 103, 108, 111, 112, 115, 119, 120, 124, 127, 132, 133, 134, 135, 139, 140, 141, 142, 143, 151, 152, 155, 156, 159, 166, 167, 168, 172, 175

Offset: 1

Author

Eric Fox, Apr 30 2022

Keywords

• nonn

Comments

These are the numbers which cannot be a clue in a Tasquare puzzle.

Tasquare also known as Tasukuea.

Examples

			A 9 clue can be satisfied in at least one way:
  OOO  OO OO
  OOO  OO9OO
  OOO9   O
So, 9 is not a term in this sequence.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Cross+A, Tasquare rules
• Nikoli, Tasukuea rules [broken link]

Crossrefs

Complement of A353202.

Cf. A022544.

Programs

Maple

q:= proc(n) local i; for i to isqrt(n) do if ormap(issqr,
      [n-i^2, n-i^2-1]) then return false fi od: true
    end:
select(q, [$1..175])[];  # Alois P. Heinz, Apr 30 2022

Mathematica

q[n_] := Module[{i}, For[i = 1, i <= Sqrt[n], i++, If[AnyTrue[ {n-i^2, n-i^2-1}, IntegerQ@Sqrt[#]&], Return[False]]]; True];
Select[Range[175], q] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz *)