B Looking for a specific periodic function

AI Thread Summary
A function that outputs 1 for multiples of a chosen number and 0 otherwise can be defined using the MOD function, where MOD(n, d) returns 0 if n is a multiple of d. The proposed mathematical expressions, including the use of the floor function and Fourier series, aim to achieve similar results but may not be straightforward. The explicit function f_m(x) incorporates a series to express periodic behavior, while the computer programming approach simplifies the task using conditional statements. Overall, the discussion emphasizes the need for clarity in defining periodic functions within natural number constraints.
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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.
 
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How about
[\ [\frac{x}{m}]-\frac{x}{m}\ ]+1
where [ ] is floor function ?
 
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anuttarasammyak said:
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
 
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}
 
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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.
 
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