B Looking for a specific periodic function

[al4n]

TL;DR

Trying to come up with a function that outputs 1 when input is some multiple of a given number and outputs 0 if otherwise.

Is there a function that outputs a 1 when the input is a multiple of a number of your choice and 0 if otherwise. The input is also restricted to natural numbers.
The only thing I can come up with is something of the form:
f(x) = [sin(ax)+1]/2
but this does not output a 0 when I want it.

 

[anuttarasammyak]

How about
[\ [\frac{x}{m}]-\frac{x}{m}\ ]+1
where [ ] is floor function ?

 

[al4n]

How about
[\ [\frac{x}{m}]-\frac{x}{m}\ ]+1
where [ ] is floor function ?

Is it mathematically sound? I generally avoid such functions because im not quite comfortable with them

 

[anuttarasammyak]

You may find Fourier series expression of the floor function e.g., in
https://en.wikipedia.org/wiki/Floor_and_ceiling_functions if it is your favour.

[EDIT] Explicitly our function f_m(x) is
f_m(x)=g_m(x)+\frac{1}{2}+\frac{1}{\pi}\sum_{j=1}^\infty\frac{\sin 2\pi j g_m(x)}{j}
where
g_m(x)=-\frac{1}{2}+\frac{1}{\pi}\sum_{k=1}^\infty\frac{\sin 2\pi k \frac{x}{m}}{k}

 

[FactChecker]

In a computer program, the MOD function, MOD(n,d), will divide one natural number, n, by another natural number, d, and return the remainder. So if n is a multiple of d, it will return a 0. So the formula (MOD(n, d) == 0) should be true (one) when n is a multiple of d and false (zero) otherwise.

If you have a particular computer language in mind, we can be more specific.