Numbers which are not the sum of distinct squares: Difference between revisions
Numbers which are not the sum of distinct squares (view source)
Revision as of 17:19, 3 February 2023
, 1 year agoAdded XPL0 example.
SqrtNegInf (talk | contribs) (Added Perl) |
(Added XPL0 example.) |
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Found 31 total in 24 ms.
</pre>
=={{header|XPL0}}==
This generates all combinations of sums of N squared up to a Limit. For
a Limit = 1000 = $3E8 = %11_1110_1000 this sums 100+81+64+49+36+16. A Limit of one million
shows that there is a huge gap following 128 of values that cannot be
generated by any combination of sums of squares. The mathematical
argument why none exist beyond 128 is provided by the Julia example.
<syntaxhighlight lang "XPL0">func SumSq(B); \Return sum of squares specified by bits in B
int B, N, Sq, Sum;
[N:= 1; Sum:= 0;
while B do
[if B & 1 then
[Sq:= N*N;
Sum:= Sum + Sq;
];
B:= B>>1;
N:= N+1;
];
return Sum;
];
def Limit = 1_000_000;
char Flags(Limit);
int I;
[for I:= 0 to Limit-1 do
Flags(I):= true;
for I:= 0 to Limit-1 do
if I < Limit then
Flags(SumSq(I)):= false;
for I:= 0 to sqrt(Limit)-1 do
if Flags(I) then
[IntOut(0, I); ChOut(0, ^ )];
]</syntaxhighlight>
{{out}}
<pre>
2 3 6 7 8 11 12 15 18 19 22 23 24 27 28 31 32 33 43 44 47 48 60 67 72 76 92 96 108 112 128 </pre>
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