Best way to determine if number is triangular number?

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Richard Crozier
Richard Crozier 2012-9-6
Hello,
I would like to test if an integer is a triangular number, and am wondering what the best way to achieve this is. I am aware that a triangular number is given by
x = n(n+1)/2
And that x is triangular if and only if 8x + 1 is a square.
However, what is the best way to actually test this in Matlab, giving consideration to floating point arithmetic?
I can think of methods like:
check x is an integer find if sqrt(8x + 1) is an integer to some floating point error
but there must be better ways.
  2 个评论
John D'Errico
John D'Errico 2012-9-6
Note that as long as 8x+1 is no more than 2^53-1, the simple test for a perfect square will be valid. And larger than that you cannot represent x exactly anyway as a double.
Richard Crozier
Richard Crozier 2012-9-6
I will only need this for relatively small numbers, it's actually a test of some user input. Useful to bear in mind though, thanks.

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采纳的回答

Matt Fig
Matt Fig 2012-9-6
istri = @(x) floor(sqrt(8*x+1))==sqrt(8*x+1);
x = 1:20;
idx = istri(x)
x(idx)

更多回答（2 个）

Azzi Abdelmalek
Azzi Abdelmalek 2012-9-6
编辑：Azzi Abdelmalek 2012-9-6
k=0
for n=1:100 %for example
x = n*(n+1)/2;
y=sqrt(8*x+1);
if round(y)==y
k=k+1;
result(k)=x
end
end
n=size(result) % you will obtain n=100, which verify the formula
or
n=1:100 %for example
x = n.*(n+1)/2;y=sqrt(8*x+1)
all(y==round(y)) % if the result is 1, the formula is checked
Sean de Wolski
Sean de Wolski 2012-9-6
  2 个评论
Richard Crozier
Richard Crozier 2012-9-6
This suggestion is fine, except that I can't actually see the solutions.
Sean de Wolski
Sean de Wolski 2012-9-6
Sure you can! You just have to get addicted to it and solve a bunch of other problems first!

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