English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we show that for any integer $a \geq 2$, each of the intervals$[a^k , a^{k + 1})$ ($k \in \mathbb{N}$) contains either $\left\lfloor\frac{\log a}{\log\Phi}\right\rfloor$ or $\left\lceil \frac{\loga}{\log\Phi}\right\rceil$ Fibonacci numbers. In addition, the density (in$\mathbb{N}$) of the set of the all natural numbers $k$ for which the interval$[a^k , a^{k + 1})$ contains exactly $\left\lfloor \frac{\loga}{\log\Phi}\right\rfloor$ Fibonacci numbers is equal to $\left(1 -\left\langle \frac{\log a}{\log\Phi}\right\rangle\right)$ and the density ofthe set of the all natural numbers $k$ for which the interval $[a^k , a^{k +1})$ contains exactly $\left\lceil \frac{\log a}{\log\Phi}\right\rceil$Fibonacci numbers is equal to $\left\langle \frac{\loga}{\log\Phi}\right\rangle$.

On the possible quantities of Fibonacci numbers that occur in some type of intervals