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dardo82/Fibonaria.tex

Created March 7, 2019 07:06
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Binary Fibonacci
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Fibonaria.tex
\begin{align*}
a,k,n,m \in \mathbb{N} \quad b \in \{0;1\} \\
A=\{a|a<2^{m}\} \quad a=\sum_{k=0}^{m-1} b_{k} \cdot 2^{k} \\
F_0=0; \ F_1=1; \ F_{n}=F_{n-1}+F_{n-2} \\
\forall k \ \ b_{k}=1 \Rightarrow b_{k+1}=0 \quad |A|=F_{m+2} \\
\end{align*}
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dardo82 commented Mar 7, 2019

La cardinalità dell’insieme dei numeri naturali minori di due alla emme la cui rappresentazione binaria non contiene due uno consecutivi è pari all’emme-più-due-esimo numero di Fibonacci.

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