Creating a Loop for Sum of Digit Squares to Equal 1

[d-star]

Hi, I'm writing a program in fortran that basically creates a loop from 1 until a certain number x (input by the user), and goes through each value between 1 and the certain number x in order to determine if each value meets certain criteria. The criteria is that the sum of the square of the individual digits created by each value in between 1 and x (where each value is taken from the preceding sum), must eventually equal 1. For example, the number 7 meets this criteria, because when we take the sum of the square of the individual digits, (7^2)=49, (4^2)+(9^2)=97, (9^2)+(7^2)=130, (1^2)+(3^2)+(0^2)=10, (1^2)+(0^2)= 1. The same goes for the number 13, except this reaches 1 after only two steps: (1^2)+(3^2)=10, (1^2)+(0^2)= 1.
I have already wrote the program for calculating the sum of the square of the individual digits of a number, and eventually reaching 1. Although I am having trouble finding a function to use in order to go through each number from 1 to a certain value x, and determining whether each number in between 1 and x meets this criteria or not.
Any help would be appreciated! Thanks!

 

[Mark44]

Hi, I'm writing a program in fortran that basically creates a loop from 1 until a certain number x (input by the user), and goes through each value between 1 and the certain number x in order to determine if each value meets certain criteria. The criteria is that the sum of the square of the individual digits created by each value in between 1 and x (where each value is taken from the preceding sum), must eventually equal 1. For example, the number 7 meets this criteria, because when we take the sum of the square of the individual digits, (7^2)=49, (4^2)+(9^2)=97, (9^2)+(7^2)=130, (1^2)+(3^2)+(0^2)=10, (1^2)+(0^2)= 1. The same goes for the number 13, except this reaches 1 after only two steps: (1^2)+(3^2)=10, (1^2)+(0^2)= 1.
I have already wrote the program for calculating the sum of the square of the individual digits of a number, and eventually reaching 1. Although I am having trouble finding a function to use in order to go through each number from 1 to a certain value x, and determining whether each number in between 1 and x meets this criteria or not.
Any help would be appreciated! Thanks!

What have you tried?

 

[gsal]

You are having trouble finding a function to use? You already wrote it! Just make a formal function out of your code and call it from within the loop of n = 1, x

 

[d-star]

alright, thanks! it actually had a suspicion that that was the case. Although I have another question as well.
I also need to integrate a way that basically identifies if each value from 1 to x satisfies the condition that its sequence eventually reaches 1, and I also need to make my program identify if the sequence does not reach 1 (goes on forever). So if the number reaches 1 it is TRUE, and if does not reach 1 (goes on forever) then it is FALSE. I then need to be able to list all the numbers between 1 and x that are TRUE(sequence reaches 1). So far I have:

PROGRAM S
IMPLICIT NONE

INTEGER :: x,j,a
READ (*,*) x
j = 1

DO a = 1,x
CALL S
j = j +1
END DO

END PROGRAM S2


(where S is my function that solves for the square of the sum of the individual digits from 1 to x, determining if each number's sequence reaches 1 or not)

Any suggestions? Thanks!

 

[LudusRex]

Hi there,

It sounds like you are on the right track with your program. In order to go through each number from 1 to x, you can use a for loop. This will allow you to iterate through each value and check if it meets the criteria you have set.

Here is an example of how you can use a for loop in your program:

do i = 1, x
! calculate the sum of the square of the individual digits for each value
! and store it in a variable called "sum"
sum = 0
num = i
do while (num > 0)
digit = mod(num, 10)
sum = sum + digit**2
num = num / 10
end do
! check if the sum eventually reaches 1
if (sum == 1) then
! if it does, print the number that meets the criteria
print*, i
end if
end do

This for loop will go through each value from 1 to x, calculate the sum of the square of the individual digits, and check if it eventually reaches 1. If it does, it will print the number that meets the criteria.

I hope this helps and good luck with your program! Let me know if you have any other questions.