What is the longest string of repeated numbers in Pi?

Question

On a brief scan of the first 100,000 digits, the longest string I could find as a string of 5 one's, which occurred about a third of the way down (nestled in this string of digits … 24658411111577583…). Does anyone know of a longer string somewhere in the first trillion, or so, digits? Is there any mathematical reason why strings of, say, hundreds or thousands couldn't occur somewhere in all of Pi?

I used the "find on this page" function on a web page to confirm that there are no strings longer that five in the first 100,000.

Oh, and by the way, HAPPY PI DAY everybody :-)

Answer 1

The string 666666666 occurs at position 45,681,781 counting from the first digit after the decimal point.

The string and surrounding digits:
86731050497515079094 666666666 71734856294979983444

I think that's the longest sequence within the first 200 million digits.

Pi is not known to be 'normal' ie each digit, or sequence of digits of a given length, appears the same amount of times, but it probably is. If Pi is normal, there is no reason why a repeated sequence does not occur somewhere, although you would have to go a long way to find it, but this may not be the case. You could easily have an irrational number that does not contain the sequence 111 (simply take Pi and remove all the 1s!)

The first link lets you search for strings in pi. The second ... basically answers your question about repeated sequences.

Answer 2

This Site Might Help You.

RE:
What is the longest string of repeated numbers in Pi?
On a brief scan of the first 100,000 digits, the longest string I could find as a string of 5 one's, which occurred about a third of the way down (nestled in this string of digits … 24658411111577583…). Does anyone know of a longer string somewhere in the first trillion, or so, digits? Is there...

Answer 3

Ten is the longest series of consecutive digits for any number within the 1st 10 billion digits. Six reaches 10 consecutive digits first, within the first billion. The numbers 2, 4, 7, & 9 only reach 9 consecutive digits within the 1st 10 billion. Nine uniquely reaches 6 consecutive digits within the 1st thousand. No other digit reaches 6 consecutive until over 100 thousand digits of Pi.

Answer 4

The poster above gives a very interesting answer, but I'll just mention there is a string of six 9's starting at decimal position 762. That's unexpected, actually - you don't have to go even 1000 positions to find a six-in-a-row.

Answer 5

You are correct in saying that one can determine pi from the area and radius or diameter as A=pi*r^2. But pi is also the ratio of the circumference of the circle to its diameter. pi = c/d so this is easily calculated with a string and ruler.