# Questions tagged [integer-sequence]

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### Estimate limit of sequence

The following sequence may have two limits, depending on the parity of $n$ as shown here: $$a_n=(1-\frac{1}{2!})^{(\frac{1}{2!}-\frac{1}{3!})^{\ldots^{(\frac{1}{n!}-\frac{1}{(n+1)!})}}}$$ I have tried ...
115 views

### I cannot get the convolution of Jacobsthal(n) and 3^n using Convolve[], DiscreteConvolve[] or ListConvolve[]

I am working on a problem where I found that the system I am working with follows OEIS A094705 which is the: "Convolution of Jacobsthal(n) and 3^n". So I have tried using the recursive formula ...
279 views

### Find sequence of sequences?

There is a function FindSequenceFunction in Mathematica, that can identify a sequence of integers based on a few first elements. But what if I have a set of finite ...
187 views

### Generating a certain sequence

I have indexed the unit cells of the Kagome lattice. Each unit cells consists of atoms $(A,B,C)$. In this cell there are $21 \times 3$ sites. From this picture above I see a pattern is emerging when ...
506 views

### Fibonacci sequence questions

I want to show that "Out of the first 450 Fibonacci numbers, the odd number is twice as many as even number." with Mathematica. Can you solve it please?
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### Finding 36 integer solutions to a set of 14 equations using various boundary conditions

What is good way to solve this system of equations? I have it run now for quite some time and it does not spit out a solution. ...
61 views

2k views

### Is it possible to invoke the OEIS from Mathematica?

I had always wondered if there might be a way to write a function, which I'll call OEISData[], that more or less works as a curated data function for The On-Line ...
133 views

### How to find a list of values of recurrence equation?

I tried with RSolve,but it fails: RSolve[{x[n + 1] == n + Sum[j*x[j], {j, 1, n}], x == 1}, x[n], n] Returns unevaluated ...
4k views

### Easier program for period of Fibonacci sequence modulo p

For a little project I need to calculate the period of a Fibonacci sequence modulo p, for which p is a prime number. For example, the Fibonacci sequence modulo 19 would be: 0, 1, 1, 2, 3, 5, 8, 13, ...
160 views

### Finding the largest palindrome which is the product of two 2-digit numbers

My goal is to find the largest palindrome which is the product of two 2-digit numbers using the following program. I want the program to add each palindrome it finds, to the list H. I also want it to ...
49 views

### A problem of a sequence and its sum

{a(n)} is such a sequence, satisfying, For all a(i) ∈ {a(n)}, a(i) =1 or -1 Let S(j) = Sum[a(i) , {i ,1, j}], then for all 1<=j<=n ,S(j)>=0. For a given n , how many {a(n)} are there?
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### How to perform this indefinite sum?

The following indefinite sum with (CC[n]=1 for even n and CC[n]=i for odd n) ...
401 views

### splitting integer problem

I want to cut the integer into small numbers and show me all the possibilities. For example, if I choose integer 6, then I would like to know how many combination of a 5 dimensional vector (or table ?)...
99 views

### Selecting integers which are not a member in an ordered list of integers

I have an ordered list of integers, i.e.: list = {1,3,5,6,8,10,12,15}; and I want to know if there is a fast way to get a list of the integers that do not appear ...
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### How to tell Mathematica to do this with decimal part of real number?

My apologies if this was asked here before. My friend and I want to do this: Suppose that we have some real number $a. a_1 a_2...a_n...$ where $a_i$ are digits in the set $\{1,2,3,4,5,6,7,8,9,0\}$ (...
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### Coefficients of polynomials forming an unimodal sequence

Let $f(x)=\sum_{i=0}^{n}a_{i}x^{i}$ be a polynomial with rational coefficients. I am interested in an efficient way which allows checking whether the finite sequence $A=(a_{i})_{i\in\{0,\ldots,n\}}$ ...
629 views

### How do I graph only integers using the list function?

I have plotted the following function using the following code: ...
113 views

### efficiently method for generating a sequence

The sequence is defined as $a(1)=1,a(n)=a(n-1)+a\left(\left\lfloor \log _2(n)\right\rfloor \right)$ A natural way do this is ...
557 views

### Evaluate large Fibonacci numbers

I want to evaluate that Fibonacci. However the result is OverFlow[]. Is there any way to evaluate it? Thank you.
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### PARI to Mathematica conversion

I need to use the coefficients T(n,k) in my algorithm and I found a program in PARI Can anybody translate this code to mathematica? ...
There is an amazing and counterintuitive theorem: For all $n$, there exists a $k$ such that the $k$-th term of the Goodstein sequence $G_k(n)=0$. In other words, every Goodstein sequence ...