0
votes
1answer
37 views

Prove a identity with Fibonacci sequence and binary sequence.

Let us: $\{f_k\}$ Fibonacci sequence; $\{u_k\}$ binary sequence i.e. $u_k=$ 0 or 1; $\rho$ real positive number. Is there a binary sequence $v_k$ such that: $$\sum_{k=2}^{n+1}\frac{u_{k-1} ...
2
votes
1answer
71 views

Recurrence relations - simple questions, please verify my answers.

I'm posting this question because this is new material for me and I am unsure of my answers and have no one to consult with. I solved the first three and would appreciate feedback. I need help solving ...
2
votes
1answer
105 views

Random infinite binary sequence

What I mean by random infinite binary sequence is an infinite sequence of $0$'s and $1$'s with probability of occurrence in this sequence equal to $1/2$ (all digits being equally likely). How is it ...
2
votes
1answer
77 views

Is there a sequence of primes whose decimal representations are initial segments of each other?

I.e., is there a sequence of primes whose decimal expansions have the following form: $$a_1,\ a_1a_2,\ a_1a_2a_3,\ a_1a_2a_3a_4, \dots$$ What about with the order of the digits reversed, so each ...
1
vote
1answer
135 views

Can every periodic binary sequence be expressed as the output of a Linear or Non-Linear Feedback Shift Register?

Quick background: The output of a Linear Feedback Shift Register (LFSR) with $n$ taps is a binary sequence which is periodic of length dividing $2^n-1$. From a mathematical point of view, such a ...
3
votes
2answers
144 views

Binary Sequence Block

More of an informatics question, rather than applied mathematics - Source - Zonal Informatics Olympiad 2011 Question Paper Although, I've tried a few brute methods, I haven't really understood ...
1
vote
2answers
191 views

A similarity measure for binary sequences from a partition

I'm onto a problem about binary sequence similarity for which I have not found any existing solution. I want to share it and the approaches I have taken, although none of them convince me. Consider a ...
0
votes
2answers
392 views

Period of a finite binary sequence

Let $G:N\to\{0,1\}$, and let $L$ be some period of $G$, so that $G(i+kL)=G(i)$. What's the best a good way to find the smallest period of $G$? I mean an algorithm that takes ($G$,$L$) and outputs the ...