pi-stat-1

Last Update 2011/12/11
©
JVSchmidt 2011

Analyzing 100.000.000.000 Decimal Digits of π

GENERAL  CONSIDERATIONS

Cuckoo Positions

It can be very interesting to explore the self referential qualities of a digit sequence. One special kind of that is a correspondence between a subsequence and its absolute position in the whole sequence.
If we find the sequence "klm...nop" exactly at position (klm...nop) we call this a CUCKOO POSITION
(German: Kuckuckszahl).

The position predicts the following sequence like the couckoo bird shouts its own name.

The first Cuckoo Position K1 is not hard to find because Pi starts with "1" at position 1 (after the decimal point):   14159265...

But where comes the next Couckoo Position and how many of them will be found amongst our
100 billion digits?

RESULTS: All Cuckoo-Position up to 100.000.000.000

cuckoo_allNumbers

RESULTS: Hits per Range

S = Sequences proofed; L = Length of Sequences
H = Hits (where ABS(Pos.-Value)<10)

cuckoo_HitsPerRange