A Harshad Number in a given number base is an integer that is divisible by the sum of its digits when written in that base.
For example, the number 11 in base 5 (which is 6 in base 10) is divisible by 1 + 1 = 2 in base 5. It is therefore a Harshad number in base 5.
1 is the first Harshad number in base 5. Let H be the 1000th Harshad Number in base 5. What are the first 3 digits of H?
To find the first 3 digits of the 1000th Harshad Number in base 5, you can follow these steps:
1. Start by listing the Harshad numbers in base 5 and find the 1000th number on the list.
2. To do this, you can start with the first Harshad number in base 5, which is 1.
3. Continue counting and checking if each number is a Harshad number in base 5. If it is, add it to your list of Harshad numbers.
4. Keep repeating this process until you have found the 1000th Harshad number in base 5.
Once you have obtained the 1000th Harshad number in base 5, you can determine its first 3 digits.
Note: This process might be computationally intensive and time-consuming if you are manually listing and checking each number. However, if you write a computer program or use a mathematical algorithm to calculate the Harshad numbers, it will be faster and more efficient.