Determine if a number is happy or unhappy and see the sequence of calculations
A happy number is a number which eventually reaches 1 when replaced by the sum of the square of each digit. If it doesn't reach 1, it's called an unhappy number.
| Step | Number | Calculation |
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The first few happy numbers are:
1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ...
For the number 19:
Since we reached 1, 19 is a happy number.
For the number 4:
Since we've reached 4 again, we're in a cycle and will never reach 1. Therefore, 4 is an unhappy number.
Happy numbers are a fascinating concept in number theory and recreational mathematics. They provide an interesting way to explore number properties and patterns.
A happy number is defined by the following process:
All unhappy numbers eventually enter a cycle of these 8 numbers:
4, 16, 37, 58, 89, 145, 42, 20, ...
The algorithm to determine if a number is happy is straightforward:
When calculating whether a number is happy, it's important to detect cycles to prevent infinite loops. All unhappy numbers eventually enter the cycle: 4, 16, 37, 58, 89, 145, 42, 20, 4, ...
Our calculator handles this by either detecting cycles or limiting the maximum number of iterations.
The concept of happy numbers can be extended to number systems with bases other than 10. A number that is happy in one base may not be happy in another.
For example, in base 2 (binary), the happy numbers start with: 1, 7, 10, 13, 19, ...
This adds another dimension to the study of happy numbers and their properties.