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

1,1

Comments

These are the numbers which cannot 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 at least one way:
  OOO  OO OO
  OOO  OO9OO
  OOO9   O
So, 9 is not a term in this sequence.

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 *)

Crossrefs

Complement of A353202.

Cf. A022544.

Sequence in context: A138615 A210254 A071780 * A305553 A338103 A190720

Adjacent sequences: A353216 A353217 A353218 * A353220 A353221 A353222

Keyword

nonn

Author

Eric Fox, Apr 30 2022

Status

approved