Gibonacci Series Limit as p approaches Infinity

To confirm the above assertion of the relationship between the Gibonacci sequences and 2n-p, we shift from the notion of p as having a specific integer value and instead examine the case of the upper boundary of p, considering the logic of p=all, or rather the integer sequence produced by starting with a 0 and a 1, then adding all the previous values of the sequence together to produced the next value in the sequence. This logic produces the following values:

0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096…

This result, expressed formally is


So we can see that the logic of the Gibonacci series ultimately leads to the aforementioned approximation of 2n-p.


Thermodynamics, Number Theory and The Goilden Ratio
Creation, Evolution and the Golden Rule
Theory of Order
Why Fibonacci and Gibonacci sequences appear everywhere in nature,
and how simple combinatoric math can describe how a Universe with simple beginnings evolved into a complex form