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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.

%I A353202 #29 Jun 28 2023 11:31:13
%S A353202 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,
%T A353202 34,35,36,37,38,40,41,42,45,46,49,50,51,52,53,54,58,59,61,62,64,65,66,
%U A353202 68,69,72,73,74,75,80,81,82,83,85,86,89,90,91,97,98,99,100
%N 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.
%C A353202 These are the numbers which can be a clue in a Tasquare puzzle.
%C A353202 Tasquare also known as Tasukuea.
%H A353202 Alois P. Heinz, <a href="/A353202/b353202.txt">Table of n, a(n) for n = 1..10000</a>
%H A353202 Cross+A, <a href="http://www.cross-plus-a.com/html/cros7tsku.htm">Tasquare rules</a>
%H A353202 Nikoli, <a href="https://www.nikoli.co.jp/en/puzzles_jp/tasukuea/">Tasukuea rules</a> [broken link]
%e A353202 A 9 clue can be satisfied in multiple ways:
%e A353202   OOO  OO OO
%e A353202   OOO  OO9OO
%e A353202   OOO9   O
%p A353202 q:= proc(n) local i; for i to isqrt(n) do if ormap(issqr,
%p A353202       [n-i^2, n-i^2-1]) then return true fi od: false
%p A353202     end:
%p A353202 select(q, [$1..100])[];  # _Alois P. Heinz_, Apr 30 2022
%t A353202 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];
%t A353202 Select[Range[100], q] (* _Jean-François Alcover_, Dec 28 2022, after _Alois P. Heinz_ *)
%Y A353202 Complement of A353219.
%Y A353202 Cf. A001481.
%K A353202 nonn
%O A353202 1,2
%A A353202 _Eric Fox_, Apr 30 2022