Request for information about basis representation

[Ralf Stephan]

> I'm interested in the algebraic properties of the set of numbers whose coefficients S are fixed but whose base varies from two to
> infinity. In the case of 35, this set is {35, 247, 1029...}, or:

The sequences 'replace 2^k with a^k in binary expansion of n'
are the square array of which your sequences form the columns.
The rows were treated in

http://www.ark.in-berlin.de/dcgfproof.ps

Hope this helps a bit,
ralf