# Tagged Questions

123 views

### Sums $\sum_{n=1}^{N}\sqrt{4n+1}$

I need to find sum of the first N terms of the sequence whose nth term is as follow : T(n)= $\sqrt{4*n+1}$ So the sequence is : $\sqrt{5}$,$\sqrt{9}$,$\sqrt{13}$,$\sqrt{17}$,$\sqrt{21}$...... ...
138 views

### How to find sum of 4th power of n numbers mod m [closed]

How can i calculate $1^{4} + 2^{4} + 3^{4} + 4^{4} .....+n^{4} \pmod m$ where $1 \le m \le 10^5$ and $1\le n \le 10^{20}$. I can't use the formula here because it will Overflow the limit of long long ...
26 views

### Understanding Sobol sequences

Can someone explain to me in simple terms, how Sobol sequences work? The wikipedia article is fairly technical. They look pretty interesting. So I shall describe (whatever little I know) in short the ...
242 views

### Solving recurrence relation: Product form

Please help in finding the solution of this recursion. $$f(n)=\frac{f(n-1) \cdot f(n-2)}{n},$$ where $f(1)=1$ and $f(2)=2$.
45 views

### Best approach or algorithm to solve equation with multiple variables?

I have an equation : $A^6x_1 + A^5x_2 + A^4x_3 + A^3x_4 + A^2x_5 + A^1x_6 + x_7 = B$ What can be the best algorithm/approach I can use to crack this? $A$ and $B$ are constants. $x_1,x_2...x_7$ are ...
505 views

54 views

### Making longest sequence

F(N) is defined as number of digits in a number N. EXAMPLE : F(123)=3 I want to make a consecutive integer sequence starting from number m (m, m + 1, ...). But to add a number n to my sequence its ...
24 views

### String satisfying the condition

Given $N$, $A_0$, $B_0$, $L_0$, $A_1$, $B_1$ and $L_1$, find a sequence S consisting only of characters '$0$' and '$1$'(a total of N characters) such that: The number of '$0$'s in any consecutive ...
84 views

### Find all distinct binary de Bruijn sequences

Messing around with numbers has lead me to the following problem, which I am struggling with. (No, not a homework question, just a problem I've thought up myself): A binary De Bruijn sequence of ...
659 views

### How to find a closed form solution to a recurrence of the following form?

I need to find the closed form solution to the following recurrence -: $T(n) = 8*T(n/2) + 0.25*n^2$ with $T(1) = 1$ and $n=2^j$ and this is what I have tried so far but just can't seem to get a ...
56 views

### Using series to produce guess for algorithm analysis

I need to find the upper asymptotic bound for the recursion: $$T(k) = 2T(k-1)+\frac{1}{k}$$ I was able to determine: The height of this tree is $k-1$. The cost of each level is ...
284 views

### Fibonacci-like sequence

Today I have to deal with something which reminds Fibonacci sequence. Let's say I have a certain number k, which is n-th number of certain sequence. This sequence however is created by recursive ...
214 views

### Number of Anti-Arithmetic sequences.

Original Problem Link. A permutation $p$ is called antiarithmetic if there is no subsequence of it forming an arithmetic progression of length bigger than $2$, i.e. there are no three indices ...
207 views

### How is “n+n/2+n/4…1” equal to “2n-1” using the formula for geometric series?

I never knew not having good knowledge of basic maths will be so crippling!! So please help me out this time. I'll be working on my maths from today on. I was discussing about complexity of an ...
89 views

### what if geometric sequence + geometric sequence

I wrote a program that basicly can find the formula of the sequence that created with any-degree equation. For example if you give my program that sequence: [1926, 2811, 833240, 28778265, 398155842, ...
67 views

### General term of this sequence

I wanted to know the General term or the function to generate this sequence I found on OEIS. It is the number of ways to express $2n+1$ as $p+2q$; where $p$ and $q$ can be odd prime number and even ...
422 views

### Convergence of a Recursive Sequence - An Example

Consider the sequence $\displaystyle x(k+1) = \frac{1}{2}\left(x(k) + \frac{a}{x(k)}\right)$ where $x(k)$ stands for the $k$th term of the sequence. What does this process converge to, and what is ...
656 views

### General McNugget problem

The classic McNugget problem states: Chicken McNuggets can be purchased in quantities of 6, 9, and 20 pieces. You can buy exactly 15 pieces by purchasing a 6 and a 9, but you can't buy exactly 10 ...
716 views

### How to calculate $1^k+2^k+3^k+\cdots+N^k$ with given values of $N$ and $k$? [duplicate]

Here $1<N<10^9$ and $0<k<50$ So we have to calculate it in order of $O(\log N)$.
262 views

69 views

### Ordered subsets summation

Let $A$ and $B$ two finite ordered sets where $A\subseteq B$. How do I count the number of consecutive and non-consecutive ocurrences of $A$ in $B$? For instance, I have nine ocurrences of set ...
124 views

### Understanding this summation identity

I'm currently reading a book in which part of the solution to the problem involve this identity: $$\sum_{j=i+1}^{n}j = \sum_{j=1}^{n}j-\sum_{j=1}^{i}j$$ Which I cannot derive myself. The only thing ...
I want to calculate the Bessel function, given by $$J_\alpha (\beta) = \sum_{m=0}^{\infty}\frac{(-1)^m}{m!\Gamma(m+\alpha +1)} \left(\frac{\beta}{2}\right)^{2m}$$ I know there are some tables that ...