p Statistics: Favourite Places
by JVSchmidt


General considerations
Could it be that on every 53th position in the p sequence we will find abnormal many "7"? Or more general in other words: does there exist a favourite distance S when stepping thru the sequence with equal steps of length S will find "much more" of digit X than of others?
To answer this we have to follow this certain number and analyze the position p of its appearences by the formula F = p mod k. In the example above k=53 and F will last from 0 to 52.
Performing this analysis for all ten digits from 0 to 9 we get k groups of 10 numbers showing the frequency of each number to be found at a "kth position" with possible additional shift from 0 to k-1.
If p is random we should find a distribution of all these groups of ten numbers near to the normal one.

It is quite enough to test p mod k for only prime numbers k, because a regularity in any other number will be reflected in the results for its prim factors.


Results
Digits analyzed: 4.2 * 10 9

Test performed for prime numbers2 - 1.009
Measured number of distribution groups76.364
Checking on a significance level of 1% (Chi2<=Chimax = 21.67)
Groups found with (Chi2>=Chimax)746
Checking on a significance level of 0,1% (Chi2<=Chimax = 27.88)
Groups found with (Chi2>=Chimax)74


Result files are very hugh so I didn't place them for download here.
If you are interested in the detailed results pls. contact me via: jvs@piworld.de

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