8
votes
1answer
299 views

Asymptotic behavior of the sequence $u_n = u_{n-1}^2-n$

I am currently interested in the following sequence: $$\begin{cases}u_0 & = & \alpha\\u_n & = & u_{n-1}^2-n\end{cases}$$ where $\alpha > C \approx 1.75793275... $ with $C$ being the ...
6
votes
0answers
309 views

Graphs with graphic imbalance sequences

Let $G$ be simple undirected graph and $e=uv\in E(G)$. The imbalance of the edge $e$ is the value $imb(e)=|d(u)-d(v)|$. Let $M_{G}$ denotes the imbalance sequence (or more correctly, multiset of ...
4
votes
0answers
323 views

Number of Configurations in the optimal Hanoi tower

There is a unique strategy how to move $n$ disks from the first rod to the second optimally and it takes $2^n-1$ steps, solution is obtained by simple recursion. I am interested into the following ...
0
votes
2answers
182 views

sequence, such that sum of any combinations in the sequence does not equal another [closed]

Hi, Is there any known sequence such that the sum of a combination of one subsequence never equals another subsequence sum. The subsequences should have elements only from the parent sequence. ...
1
vote
1answer
280 views

Maximal difference between k randomly drawn numbers from 1 to n – Looking for formula to sequence

Hello! I have an interesting problem that seemed simple to me, but I'm unable to solve it on my own. Suppose I am drawing k numbers out of n numbers labeled from 1 to n. Considering all ...
-3
votes
2answers
641 views

An interesting, simple, sequence - surprised to find little material. [closed]

I've been considering this sequence: $$1,2,3,6,12,24,48,96,192,...$$ I've generated the sequence from the rule $$V_n=\sum_{0\leq i \lt n} V_i$$ $$V_0=1; V_1=2V_0=V_0+V_0$$ What interests me most, ...
18
votes
3answers
1k views

Zeroes of the random Fibonacci sequence

Let X_n be the "random Fibonacci sequence," defined as follows: $X_0 = 0, X_1 = 1$; $X_n = \pm X_{n-1} \pm X_{n-2}$, where the signs are chosen by independent 50/50 coinflips. It is known that ...
5
votes
5answers
598 views

Can an integer or rational sequence satisfy some bounded order recurrence $\mod \ $ almost all primes but doesn't satisfy such in $\mathbb{Q}$?

Can an integer or rational sequence satisfy some bounded order recurrence $\mod \ $ almost all primes but doesn't satisfy such in $\mathbb{Q}$? The recurrences $\mod p$ can be different, possibly ...
10
votes
11answers
2k views

Longest coinciding pair of integer sequences known

There are arbitrarily many pairs of integer sequences (of arbitrary origins) that coincide upto an $N$ but differ for an $n > N$. I assume, the coincidence will be considered accidentally then by ...