lucas cycle construct
lucas cycle A+B
master lucas cycle
Repeating cycles of modulo values derived from the Lucas series.
selection of working data:
Modulo 9 (mod9) Pisano Period of 24
Master Lucas Cycle construction - breakdown of values.
[Notice how the Lucas series is developed out of the Fibonacci series by alternate addition of Fibonacci values]
[Notice also the framework nature of 3-6-9-0 values, in red]
Processing in Modulo 9 (mod9) is commonly termed transposing to the Vedic Digital Root. It is used in Numerology.
'Casting out the Nines' is a technique introduced to Europe at the same time as the Fibonacci Series. This technique can only refer to Modulo 9 processing where 9 is equivalent to 0.
Below I tabulate all but one of the possible Modulo 9 additive series.
(I ignore the 0-9 Series since all values are 9 aka 0).
Notice a Reciprocal / Reflective pattern.
Column 1 = Series 1-8 is the Fibonacci Series (Yellow - Pink).
The Lucas series pattern of Modulo 9 digits is found in the
Column 2 = Series 2-7 (Beige - Pale Green) &
Column 7 = Series 7-2 (Pale Green - Beige),
However there is a precise order of unalterable values in Lucas which exempts it from this table. Lucas values are locked in to both Fibonacci values & exponential Phi values.
All one can say is that the Lucas Series is of a class (2-7), (7-2) additive series.