Thread: recurring digits

In an irrational number what is the longest possible sequence of a single digit that can occur?

Originally Posted by anthp1234

In an irrational number what is the longest possible sequence of a single digit that can occur?

In almost all irrationals a string of 's will occur that is longer than for all in .

Google for normal numbers.

CB

Just by using the word "irrational" you automatically attach absolutely no general rules to the decimal expansion of the number. Here is a simple proof.

Define as follows:

The first digits of are . After this string of 's terminates, the next digits are exactly the digits of .



This number is automatically irrational because it has an infinite non-repeating decimal expansion, and yet n can take on whatever value you choose, whether it be 20 or 20 trillion.

Ok, just consider , what is the longest string of a single recurring digit in ?

Originally Posted by anthp1234

Ok, just consider , what is the longest string of a single recurring digit in ?

Already answered in 2nd post in this thread, \pi is believed to be normal (though not proven so), so there is no longest string of a single digit in its' decimal expansion.

CB