Fractalforums

Maybe it is not the best place to post this. There could be some existing thread were it could fit.

Jean-Francois Colonna - Number Theory
gallery

https://imaginary.org/gallery/jean-francois-colonna-number-theory

This is nice:

The additive persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-.

Starting from the origin of the coordinates (at the center of the picture), one follows a square spiral-like path and numbers each integer point encountered (1, 2, 3,…).

Then one displays the N-th point with the false color f(PA(N,B)) where:

PA(N,B) = the additive persistence of N for the base B,
f(...)  = an arbitrary ascending function

Let’s define PA(N,B) with an obvious example:

B = 10
N = 856 (= 8xB^2 + 5xB^1 + 6xB^0)

Then the following sequence is computed:

856 ---> (8+5+6) = 19 ---> (1+9) = 10 ---> (1+0) = 1

It takes three (3) steps to reach a one digit number. Then:

PA(856,10) = 3



and

The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-.





The Goldbach conjecture -the Goldbach comet or the Goldbach rainbow- from 6 to 411678.
Lots to explain what it is. I hadn't read the whole scientic page about this so I can't.


p.s.
Not fractal https://eyewire.org/

Linkback: https://fractalforums.org/share-a-fractal/22/jean-francois-colonna-number-theory/1897/

Interesting.