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# Questions tagged [integer-sequences]

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

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### What do we know about Lucky numbers?

I'm really fascinated by lucky numbers (Wikipedia; OEIS A000959) and their prime-like characteristics. They have their very own Goldbach, Legendre, Lemoine and twin conjectures. I was wondering ...
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### Asymptotic analysis of a peculiar sum of squares sequence

Let $a,b$ be two positive integers. Let the sequence $\{s_n\}_n$ be the set of all possible sums of squares $a^2+b^2$, such that they are in ascending order \begin{align*} & n=1 & s_1=1^2+1^2=...
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### Are there infinitely long arithmetic progressions in every increasing sequence of positive integers with bounded gaps between consecutive terms?

Suppose the largest gap is D>1 and at least two of the gaps 1,2,...,D appear infinitely many times. I think the answer is NO. But I find it difficult to formulate a necessary and sufficient ...
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### How many non-isomorphic, simple, connected graphs with 6 vertices are there? [closed]

A graph is called simple if there are no loops and there are no multiple edges. Is it possible to compute the number of non-isomorphic, simple, connected graphs with 6 vertices? If the number is known,...
$\{b_n\}_{n\geq0}$ is a number sequence satisfying the following condition: \begin{equation} b_{m}=\sum_{r=0}^m\sum_{h=0}^r\left(\frac{m!}{(m-r)!(r-h)!h!}\right)^2b_{m+h-r}b_{r},~\forall m\in\...