Look below for a table of the pitches of the first 1K positions of the infinity series presented as 3 (expandable) images.
If we take the first 10K pitches and explore them for pitch repetition we get the following:
C# = 1,129 C = 1,129
D = 1,036 B = 1,036
D# = 926 A# = 926
E = 740 A = 740
F = 631 G# = 631
F# = 538 G = 538
filters may be used to explore other quantities for symmetry.
and here is a link to some fascinating work by Stefaan Himpe (many thanks for your contribution)
https://notebooks.azure.com/sluimermuis/projects/pernorgard/html/InfinitySeries-Copy.ipynb
and here is (I hope) some useful tables of pitches for those - like me - of a more musical - and less mathematical outlook.
An excel table of the first 100k places is available on request, just post a contact in the comments column.
