Eliminate multiple of couple of numbers - fortran

Question

I have this simple program that create a list of two digit from 1 to 7:
1 1
1 2
1 3
1 4
...
and so on.
The condition I want is complicated because I want to EXCLUDE multiples of the two numbers: if I have 1,2 printed I don't want also 2,4 . And so on.
The f90 program is very simple:
program multiple
implicit none
integer :: i,j
i=0
j=0
do i= 1,7
do j =1,7
print*, i,j
end do
end do
end program
The question is: what IF (or other criteria) I must implement to eliminate digits of the form:
2 4
2 6
3 6
that are the multiples of 1,2 ; 1,3 ; 1,2 ?

Answer 1

If the largest value that either digit can take is 7 this ought to work:
Rewrite each pair of digits as a rational number with denominator 5040. I leave it as an exercise to figure out why I chose that denominator. So (2,3) would become 3360/5040. Of course, since the numbers have a common denominator you don't need to store that.
Now you have a mapping from your list of pairs to a list of integers; all the pairs which are equivalent by your rule (ie (1,2),(2,4),(3,6), ...) map to the same integer (in this case 2520).
There is a variety of ways to use this list of integers to write a loop to print only one of the pairs which maps to it.
This should be enough to get you started. If you have problems turning this into Fortran update your question with your best attempt and I (or someone else) will help you finish it.

Answer 2

I'm not entirely clear on the specifics, but it's simple enough to just show the general case.
In simple terms, i is your "outer loop" and first number, and j is your "inner loop" and second number. If you want to skip pairs containing a specific second number, the if goes around the print statement. If you want to skip pairs containing a specific first number, the if goes around the inner loop.
But, you want to skip the loop if the index is not your target value.
To see what both looks like in a program (2, 5, 3, and 6 could be any numbers):
do i= 1,7
if i /= 2 .and. i /=5 then
do j =1,7
if j /= 3 .then. j /= 6 then
print*, i,j
end if
end do
end if
end do
So, in this case, you'll only execute the j loop when i isn't 2 or 5. When you execute the inner loop, it will only print when j isn't 3 or 6.

Answer 3

Another approach would be to declare an array of logicals, such as
logical, dimension(7,7) :: found
Set every element to .false.. Then read your list of pairs of numbers. When you encounter a pair such as (2,4) you first reduce the fraction it represents (ie to (1,2)), then you set the corresponding element of found to .true..
After one run through your list of pairs of integers the array found contains .true. at precisely those locations whose indices are the pairs you are looking for.
This doesn't quite work if your list contains, say, (2,4) and (3,6) but not (1,2) and your desired output is (2,4), that is the first of the pairs which occurs. But I expect you could adapt it for this situation too.