# Questions tagged [integer-sequence]

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### How can I program the last digits of Fibonacci numbers?

Is there a way to compute the last digits of an arbitrarily large Fibonacci number? For the $10^n$th Fibonacci number, we can just find the $2^n$-th Fibonacci number (if that isn't too large) $\bmod n$...
61 views

### 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 ...
122 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 ...
162 views

### 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. ...
65 views

83 views

### The next element can be obtained using Predict or SequencePredict?

I want to estimate the next number with the data of the sequence listed as elements 0 and 1. For example, when data = {0,0,1,1,0,0,1,0,0,1,1,0,0,1} (actually, ...
137 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 ...
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?
72 views

### How to perform this indefinite sum?

The following indefinite sum with (CC[n]=1 for even n and CC[n]=i for odd n) ...
403 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 ?)...
100 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 ...
703 views

### 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 $\{1,2,3,4,5,6,7,8,9,0\}$ (...
64 views

### 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 $A=(a_{i})_{i\in\{0,\ldots,n\}}$ ...
750 views

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

I have plotted the following function using the following code: ...
114 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 ...
573 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.
163 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 ...
109 views

### Simplifying/re-expressing a generating function for an integer sequence using Mathematica

Consider the sequence of natural numbers generated by: $f(n) = 2 n + (-1)^n/2 - 1/2$, for $n > 0$ and $n \in \mathbb{Z}^+$ (positive integers): i.e., {1, 4, 5, 8, 9, 12, 13, 16, 17, 20, ...} ...
92 views

### Producing a particular sequence of integers recursively [closed]

I am supposed to write a function which computes the next integer in a sequence from the given one. For example: nextval should give mm ...
78 views

### 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? ...
163 views

### How many terms does FindSequenceFunction need to discover a simple polynomial rule?

Consider a simple sequence starting with seq1 = {429, 1014, 1935, 3264, 5073, 7434, 10419, 14100, 18549, 23838}; We are looking for a rule (of course there ...
900 views

### Partitioning a number into consecutive integers

Consider n=45; then $$1+2+3+4+5+6+7+8+9=45$$ $$5+6+7+8+9+10=45$$ $$7+8+9+10+11=45$$ $$14+15+16=45$$ $$22+23=45$$ Question: how to find all representations of a ...
117 views

### Why does the FindSequenceFunction command sometimes succeed with subsequences, while failing for the longer sequences?

I've encountered this phenomenon a number of times--and can provide specific examples if requested. For example, I have a 75-long sequence of rational numbers for which the FindSequenceFunction fails ...