# where to start?

I'm new here and I'd like to contribute some of my mathematical inventions/discoveries:
*The guyot function, an infinitely differentiable function whose Taylor series doesn't converge, or does converge but not to the function, arising as the density function of a stochastic process. This could go in pathological functions or probability.
*64-100 sequences. I just batted out a GMP program to compute them (some of them go to hundreds of digits). I have a conjecture, but haven't investigated them deeply.
*The halftone function, if I can recreate it (it was on a stolen laptop).
Should I put them in the encyclopedia, in papers, or where? Where should I put the computer programs?

### Re: where to start?

The sequences are A081880 in the OEIS. I submitted them several years ago.

The halftone function does indeed relate to halftone imaging, but as far as I can tell from Google, no one has come up with that particular function. I remembered how I constructed it; it's actually a family of functions, though I didn't know it then. I'm thinking of calling the article "Family of Ideal Halftone Functions" or the like. It's a function f(x) such that f(x)*f(y) is a halftone spot function. In actual halftoning they use other functions, such as sin(x)sin(y), apply a correction function to the darkness, and rasterize the function for speed.

### Re: where to start?

I would start by making sure that I have really invented something by looking at the applicable books and periodicals. I have invented lots of things, only to then discover that other amateurs beat me to the punch by hundreds if not thousands of years.

For the sequences, I would look each of them up in the OEIS. If they're not in there and you can foresee other researchers wanting to know about them, I would submit them there.

Does your halftone function have anything to do with halftone imaging like what newspapers use? You might want to try Googling "halftone function" to see if maybe someone else already came up with your halftone function.

Lastly, I want to emphasize that I'm a math amateur. A few amateurs like Fermat and Heegner have come up with great things. But for every Heegner there is a dozen of PrimeFans and a gross of crackpots who think they have squared the circle or solved the Riemann hypothesis.