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

1,2

Comments

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

Tasquare also known as Tasukuea.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cross+A, Tasquare rules

Nikoli, Tasukuea rules [broken link]

Example

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

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 *)

Crossrefs

Complement of A353219.

Cf. A001481.

Sequence in context: A039216 A336109 A091208 * A068398 A293168 A133194

Adjacent sequences: A353199 A353200 A353201 * A353203 A353204 A353205

Keyword

nonn

Author

Eric Fox, Apr 30 2022

Status

approved