Best way to determine if number is triangular number?

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.

[John D'Errico]

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]

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.

Answer 1

[Matt Fig]

istri = @(x) floor(sqrt(8*x+1))==sqrt(8*x+1);
x = 1:20;
idx = istri(x)
x(idx)

[Richard Crozier]

I think this is the best for my purposes, thanks!

Answer 2

[Azzi Abdelmalek]

 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

Answer 3

[Sean de Wolski]

CODY!

[Richard Crozier]

This suggestion is fine, except that I can't actually see the solutions.

[Sean de Wolski]

Sure you can! You just have to get addicted to it and solve a bunch of other problems first!