# Questions tagged [integer-sequences]

For questions about sequences of integers. References are often made to the online resource oeis.org.

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### A finite alternating sum

We have stumbled upon the following finite alternating sum, which we have trouble analyzing. The sum is: $$S_n = \sum_{j=0}^n \frac{ (-1)^j e^{-j} }{j!} (n-j)^j$$ We have observed numerically that ...
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### Does the Kimberling sequence map numbers “arbitrarily far away”?

The Kimberling sequence is a recursively defined "shuffling sequence" (pictorial description here). Let $k:\mathbb{N}\to \mathbb{N}$ be the Kimberling sequence. Does $k$ map members of $\mathbb{N}$ ...
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### A problem inspired in the definition of tau numbers and a divisibility relationship related to powers of two

It is (I assume that this easy fact is well-known) obvious that an integer $n>1$ is a power of two $n=2^{\alpha}$, where $\alpha\geq 1$ is integer, if an only if $n$ satisfies the divisibility ...
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### Is there a name for this operation on integer functions?

Suppose $f$ and $g$ are functions from $\mathbb N^+$ to itself. I want to consider the function $f^g$, where $f^g(n) = f \circ \dots \circ f(n)$, where composition is done $g(n)$-many times. Note ...
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### The growth of a sequence related to Liouville numbers [closed]

I am doing a work on Liouville numbers. The Liouville constant $\ell=\sum_{k\geq 0}10^{-k!}$ has its approximation by rational numbers related to the fact that for $v_n=n!$, then $v_{n+1}/v_n$ tends ...
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### Two conjectures inspired from an equation involving the sum of divisors and the Euler's totient function due to Iannucci

In this post I add two equations involving the sum of divisors $\sigma(n)$ and the Euler's totient function, denoted in this post as $\varphi(n)$, and after I ask about a conjecture involving these. ...
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### Squares in Lucas sequences

Good night, everyone! According to a celebrated result by J. H. Cohn, the only perfect squares in the Fibonacci sequence are $F_{0}=0$, $F_{1}=F_{2}=1$, and $F_{12}=144$. It is also known that the ...
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