User:Bennibeadif/sandbox

= The Bennibeadif function =

The sequence {1, 3, 7, 11, 19, 23, 35, 43, 55, 63 ...} is generated with the function $$B: \mathbb{N}_1\rightarrow \mathbb{N}_1$$defined as $$B(n)=|\mathbb{B}_n|$$

where

$\mathbb{B}_n=$ $$\begin{cases} \left \{ \frac{1}{1} \right \}, \qquad \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad \qquad\,\,\,\,\,\,\,\,\,\,\,\text{for }n=1 \\

\left \{\mathbb{B}_{n-1}\,\cup\,\left \{ \tfrac{m}{n},\tfrac{n}{m}\in\mathbb{Q}\,\, \vert\,\, m\in\mathbb{N}_\leq (n) \land\gcd(m, n) = 1 \right \} \right \},\,\,\, \text{for }n>1

\end{cases}$$