10989

10989 is a sequence of numbers that has gained attention in recreational mathematics and online communities. It is generated by a simple iterative process. Starting with a given integer, the process involves calculating the sum of the squares of its digits. This sum then becomes the next number in the sequence. The process is repeated indefinitely.

For example, if we start with the number 19:

1^2 + 9^2 = 1 + 81 = 82.

The next number in the sequence is 82.

Repeating the process for 82:

8^2 + 2^2 = 64 + 4 = 68.

The next number is 68.

Repeating for 68:

6^2 + 8^2 = 36 + 64 = 100.

The next number is 100.

Repeating for 100:

1^2 + 0^2 + 0^2 = 1 + 0 + 0 = 1.

The next number is 1.

Repeating for 1:

1^2 = 1.

The sequence has now entered a cycle, repeating the number 1 indefinitely.

The number 10989 itself does not hold any inherent mathematical significance beyond being a potential starting point or an intermediate value in such sequences. The interest in this specific sequence often stems from its behavior: whether it terminates in a cycle, or if it tends towards infinity. Many starting numbers will eventually lead to a cycle. Some famous cycles include the cycle involving 1 (as shown above), and another cycle involving 4, 16, 37, 58, 89, 145, 42, 20, and 4. Numbers that eventually reach 1 are often referred to as "happy numbers."