cp's OEIS Frontend

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.

%I A353219 #20 Jun 28 2023 11:28:04
%S A353219 7,12,15,22,23,24,28,31,39,43,44,47,48,55,56,57,60,63,67,70,71,76,77,
%T A353219 78,79,84,87,88,92,93,94,95,96,103,108,111,112,115,119,120,124,127,
%U A353219 132,133,134,135,139,140,141,142,143,151,152,155,156,159,166,167,168,172,175
%N 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.
%C A353219 These are the numbers which cannot be a clue in a Tasquare puzzle.
%C A353219 Tasquare also known as Tasukuea.
%H A353219 Alois P. Heinz, <a href="/A353219/b353219.txt">Table of n, a(n) for n = 1..10000</a>
%H A353219 Cross+A, <a href="http://www.cross-plus-a.com/html/cros7tsku.htm">Tasquare rules</a>
%H A353219 Nikoli, <a href="https://www.nikoli.co.jp/en/puzzles_jp/tasukuea/">Tasukuea rules</a> [broken link]
%e A353219 A 9 clue can be satisfied in at least one way:
%e A353219   OOO  OO OO
%e A353219   OOO  OO9OO
%e A353219   OOO9   O
%e A353219 So, 9 is not a term in this sequence.
%p A353219 q:= proc(n) local i; for i to isqrt(n) do if ormap(issqr,
%p A353219       [n-i^2, n-i^2-1]) then return false fi od: true
%p A353219     end:
%p A353219 select(q, [$1..175])[];  # _Alois P. Heinz_, Apr 30 2022
%t A353219 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];
%t A353219 Select[Range[175], q] (* _Jean-François Alcover_, Dec 28 2022, after _Alois P. Heinz_ *)
%Y A353219 Complement of A353202.
%Y A353219 Cf. A022544.
%K A353219 nonn
%O A353219 1,1
%A A353219 _Eric Fox_, Apr 30 2022