I just need to get this stuff out of my head and this is probably a better place to do it than in(yet another) notebook.

 

A + A' = B

f(x) + r(x) = B

f(x) != r(x) or f(x) = r(x) - Dependent on base and x.

 

 

Mixed base series possible consisting of only palindromic numbers.

 

ie. 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33...

and no, I have no idea what use any of this would ever be. I keep thinking cryptography, but not sure how that would go.

 

Is non-palindrome forming mixed base possible? Unknown at present.

It seems you don't know whether you are coming or going.

I exist in a state of superposition with my selves

 

Yeah, has been a bit crazy as of late.

 

 

Basic idea stems from base conversion. If you can convert something to 14, a slightly modified function can convert that to 41.

 

Some numbers convert the same for both functions, 55 for example(depending on the base).

 

Mainly hoping that looking into the general form will yield some insight. Passes the time at any rate.

Edited November 9, 201510 yr by Endy0816

[latex]\sum_{i=0}^{n}(a_{n-i} * b^{i})[/latex]

 

Works for an initial value in the form: a_na_n-1a_n-2 ... a₀ tested for base 10.

 

456 -> 6*10² + 5*10¹ + 4*10⁰ = 654

 

...and yes, I'm butchering things a bit here...