Analyzing chains that hold only different digits
GENERAL CONSIDERATIONS / EXPECTED VALUES
Dividing data into substrings of length L we can test whether all digits in a substring are different or not. It is clear that max length of substring with nonrepeating digits in decimal presentation is 10. The chance to find a 10 digits long nonrepeating sequence is very poor - 0,0363%. Anyway, the first max sequence in Pi is already found at position 60: ...4592307816...
We gonna test the frequencies of nonrepeating digits for L=2 to 10.
The expected frequencies for different values of L are
L=3: 9/10 * 8/10
L=4: 9/10 * 8/10 * 7/10
L=10: 9/10 * 8/10 * 7/10 * ... * 2/10 * 1/10
and in general w(L)=9!/(10-L)!/10L-1
Critical Value of Chi2-Distribution on 99,5% Level (f=1): 7,879