Exodies wrote:What's the longest sequence of the first n digits of pi seen after the first digit?
(Shirley you could have expressed that better, Exo?)
I don't know, but we have only calculated the smallest part of pi. About 5 trillion digits at a recent count. Not very much. You can search on the web for longest sequence of 9's yet found and such like.
Oh yes. You can search on the net.
Counting from the first digit after the decimal point. The 3. is not counted.
3 occurs at position 9
31 occurs at position 137
314 occurs at position 2,120
3141 occurs at position 3,496
31415 occurs at position 88,008
314159 occurs at position 176,451
3141592 occurs at position 25,198,140
31415926 occurs at position 50,366,472
314159265 did not occur in the first 200000000
So in the first 200 million, the answer is eight. Which is the same answer for runs of the digit 1 (11111111 occurs at position 159,090,113).
Do all 8 digit patterns occur in this range? What's the fastest algorithm (on a MIX machine) to answer this question?
Coolest thing I came across while googlebinging this is:
In 1996, NERSC's David H. Bailey, together with Canadian mathematicians Peter Borwein and Simon Plouffe, found a new formula for pi. This formula permits one to calculate the n-th binary or hexadecimal digits of pi, without having to calculate any of the preceding n-1 digits. This formula was discovered by a computer, using Bailey's implementation of Ferguson's PSLQ algorithm.
Thanks for not misreading the question, Grumbs.