A353202 Positive integers which can be expressed as the sum of three or fewer squares, no more than two of which are greater than 1.

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 14, 16, 17, 18, 19, 20, 21, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 45, 46, 49, 50, 51, 52, 53, 54, 58, 59, 61, 62, 64, 65, 66, 68, 69, 72, 73, 74, 75, 80, 81, 82, 83, 85, 86, 89, 90, 91, 97, 98, 99, 100

Offset: 1

Author

Eric Fox, Apr 30 2022

Keywords

• nonn

Comments

These are the numbers which can be a clue in a Tasquare puzzle.

Tasquare also known as Tasukuea.

Examples

			A 9 clue can be satisfied in multiple ways:
  OOO  OO OO
  OOO  OO9OO
  OOO9   O
		

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 A353219.

Cf. A001481.

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 true fi od: false
    end:
select(q, [$1..100])[];  # 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[True]]]; False];
Select[Range[100], q] (* Jean-François Alcover, Dec 28 2022, after Alois P. Heinz *)