# Zeros between [a, b]

## Main Question or Discussion Point

Dear all,

Can anybody tell me if there is any mathematical way to know how many zeros between a and b, where we should consider all the numbers between them (inclusive).

E.g.

a = 10,
b = 12,

numbers in between: 10, 11, 12

Thus, the answer is --> 1

I made a simple program to do this for me by looping and incrementing, but as the numbers become bigger, it take "long" time to get the result.

Thus, math theories might be the solution for such problem.

Thanks

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Yes, and it is simple. Use a combinatorial aproach.

HallsofIvy
Homework Helper
Dear all,

Can anybody tell me if there is any mathematical way to know how many zeros between a and b, where we should consider all the numbers between them (inclusive).

E.g.

a = 10,
b = 12,

numbers in between: 10, 11, 12

Thus, the answer is --> 1

I made a simple program to do this for me by looping and incrementing, but as the numbers become bigger, it take "long" time to get the result.

Thus, math theories might be the solution for such problem.

Thanks
I don't understand what you mean. When you say "zeros" I assume you mean the zeroes of some function, but your example appears to be how many integers there are between two given integers.

Dear all,

Can anybody tell me if there is any mathematical way to know how many zeros between a and b, where we should consider all the numbers between them (inclusive).

E.g.

a = 10,
b = 12,

numbers in between: 10, 11, 12

Thus, the answer is --> 1

I made a simple program to do this for me by looping and incrementing, but as the numbers become bigger, it take "long" time to get the result.

Thus, math theories might be the solution for such problem.

Thanks
If you mean look at each number as a string and count how many characters are zero I think you should try for solving in general generate a(n) = the number of zeros in [1, n] then [b,c] = a(c) - a(b-1). See http://www.research.att.com/~njas/sequences/A061217 [Broken]

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HallsofIvy