The structure of numbers of representation
Abstract
When the sequence of numbers of representation (RN) will be divided where the numbers of representation are (relatively) low a structure appears. This is when the position equals the Lucas sequence.
All the numbers of representation are part of a sequence that has a Fibonacci based relation for as well the value of the numbers of representation as the position in the sequence: the double related sequences. These double related sequences (Rf) are shown more in detail using different colours to highlight them.
It appears that RN is based a structure of units of six Rf‘s. Starting at row 5 these units develop in a rhythm of a Fibonacci word.
It is also possible to create such a unit of six double related sequences at the first four rows. This unit has some minor differences to the other units.
Finally the structure of RN written out for the rows 1-14.
- 1 A structure appears
- 2 More in detail
- 3 The structure of the units of six R(f)'s
- 4 The first four rows
- 5 The structure of R(N)
