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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.
3
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
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
KEYWORD
nonn
AUTHOR
Eric Fox, Apr 30 2022
STATUS
approved