pi-stat-1

Last Update 2011/12/11
©
JVSchmidt 2011

Analyzing 100.000.000.000 Decimal Digits of π

GENERAL CONSIDERATIONS / EXPECTED VALUES

Nonreapeting Digits

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.
They expected frequencies are for
L=2: 9/10
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

RESULTS

Critical Value of Chi2-Distribution on 99,5% Level (f=1): 7,879

nonrepeating_details