Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

how many $1$s are there in the first n digits of $\pi$? Any good approximation of its distribution? How about the place of the $n$th $1$? Are these two questions related?

share|cite|improve this question
I think about $[n/10],$ no? – Leox Dec 22 '13 at 19:10
up vote 10 down vote accepted

The answer is not known, but it is conjectured that $\pi$ is simply normal in base $10$, and from that you would expect one tenth of the digits to be $1$s, and the $n$-th $1$ to be found near digit number $10n$, for huge values of $n$, in some sense.

share|cite|improve this answer

See also OEIS sequence A037000

share|cite|improve this answer
Thanks, very interesting link – Kavim Dec 22 '13 at 21:04

There is no known answer to this question.

share|cite|improve this answer
The exact number, as a function of $n$ is not known. There are partial answers on the question of the distribution of digits. – Yiorgos S. Smyrlis Dec 22 '13 at 19:26
@DietrichBurde It is not even known if there are infinitely many $1$s or not. – Jeppe Stig Nielsen Dec 22 '13 at 19:33
I see. Thank you. – Dietrich Burde Dec 22 '13 at 19:34
(To comment) What partial answers are there? – Jeppe Stig Nielsen Dec 22 '13 at 19:38

Actually, yes, Kavim, since $\pi$ is suspected (though not yet proven) to be a normal number. As n grows large, the ratio is approximately $\dfrac1{10}$ for each digit. All computations done so far, even up to over a trillion digits, confirm this conjecture.

share|cite|improve this answer
the ratio is >> the ratio would be. – Did Dec 22 '13 at 23:38

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.