Questions tagged [integer-sequence]
The integer-sequence tag has no usage guidance.
102
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Nested sequence evaluation seems to fail [closed]
I tried do define two OIES Sequences like that:
...
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0
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35
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Coloring cells created by a graph [duplicate]
A few days ago, an article by N. J. A. Sloane appeared on arxiv.org: https://arxiv.org/pdf/2301.03149.pdf, about the history of the On-line Encyclopedia of Integer Sequences. One of the problems ...
- 5,147
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Writing a number 'm' as a sum of 'n' prime numbers
We can write {2 = 2}, {3 = 2+1, 3 = 3}, {4 = 2+2, 4 = 3+1}, {5 = 3+2, 5 = 2+2+1}, {6 = 3+3, 6 = 5+1, 6 = 3+2+1} and so on. I am trying to write every positive integer as a sum of Prime numbers.
In ...
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Subsequences with distinct values
(this question was modified after initial answers)
For a sequence
x = {6,4,2,4,2,4,6}
y = Subsequences[x]
gives the list of ...
- 493
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0
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67
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Calculate an n-order determinant by FindSequenceFunction
Calculate an n-order determinant:
$\left|\begin{array}{cccccc}1 & 2 & 3 & \cdots & n-1 & n \\ n & 1 & 2 & \cdots & n-2 & n-1 \\ n-1 & n & 1 & \cdots ...
- 1,719
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How can I convert sequences to sharings and vice versa?
Given positive integers $k,n$, a $k$-sequence of $I_n$ is a list of $k$ not necessarily distinct elements of $\{1,\dots, n\}$. And an $n$-sharing of $I_k$ is a list of $n$ possibly empty, disjoint ...
- 359
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Is there a Mathematica function that generates all ordered partitions?
My book defines a length $k$ ordered partition of $I_n$ as a sequence of $k$ disjoint, possibly empty subsets of $\{1,\dots, n\}$ that union up to $\{1,\dots, n\}$. Is there a mathematica function ...
- 359
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120
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Generate a sequence of all cases
There is a sequence of numbers that satisfies
$a_1=2$, $a_n-a_{n-1}\in \{1,3,5\}$
I tried to enumerate all possibilities using the code below
...
- 5,404
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0
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71
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“Largest” symbolic common factor of an integer sequence (not simply GCD)
Suppose, I have a finite fragment of a quickly increasing sequence of integers $\{a_n\}$ that is too complex, unusual, or irregular for FindSequenceFunction to find ...
- 7,058
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Is there a feasible way to passively crosscheck sequences against the OEIS database?
What this questions is not: Can I access OEIS from Mathematica?
This topic has been raised more than once and has been well addressed.
Here's the situation as it seems to me:
OEIS is a tremendously ...
- 753
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137
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Faster way to generate a sequence of numbers
There is a sequence of Numbers that satisfies
(1) $a_1+p\geq 0, a_2+p=0, p\in R$
(2) $a_{4n}>a_{4 n-1}, (n=1,2,...)$
(3) $a_{m+n}\in\{a_m+a_n+p, a_m+a_n+p+1\}, (m,n=1,2...)$
I tried to list the ...
- 5,404
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140
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Exponential Decay fit and printed parameters with integer data [closed]
Problem:
I'm trying to plot an exponential decay curve on a set of integer data, and print the various parameters and their uncertainties on the plot itself. Having adapted code from another question, ...
- 505
3
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209
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Using dynamic programming to compute an integer sequence
Let a[n] = n + 1 - a[EulerPhi[n]], n integer > 0. I have Python code that generates the sequence using dynamic programming. How can I achieve the same thing elegantly/idiomatically in Mathematica?
...
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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) $\bmod n$...
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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 ...
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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 ...
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2
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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.
...
- 1,911
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2
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Solving a big system of equations using certain conditions
I have the following problem: I want to solve a big system of equations for a certain number of variables which I call $a_k$, the variables need to satisfy the following conditions: all $a_k\in\mathbb{...
- 1,911
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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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2
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119
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Generate a sequence of primes giving position and value of a digit in its digit-decomposed version
The prime sequence starts:
...
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76
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How to sort Dataset where each row include a sequence of strings and integers
I got this type of data :
...
- 33
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247
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Solve transcendental equation involving a built-in function [closed]
How can I solve an equation of the following form?
$$x = 10+\mathrm{\mathbf{PrimePi}[x]}$$
where $x$ is an integer. I am using Solve but am getting the following ...
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76
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Finding sequence limits from matrix determinants
I have a problem whereby I want to calculate the limit of a sequence of determinants of matrices of increasing dimensions using the DiscreteLimit command. To illustrate this, I use an example with a ...
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7
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3
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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 ...
- 549
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208
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Generating number sequence
I am very new to mathematica. I am trying to generate list of number sequence.
I want to make 6 sequences. 1 - 10, 10 - 100, 100 - 1 000, 1 000 - 10 000, 10 000 - 100 000. All reversed. Is there any ...
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Accessing internal calculations of Mathematica code
For a given Mathematica program that generates a sequence x of integers, is it possible to also generate equal length sequences of integers that were used internally by the Mathematica kernel to ...
- 493
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2
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267
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solve for two variables for each n related to Collatz conjecture
For this code, for each x I would like to solve for all value ranges for c1 and c2 in a bounded range ie c1 and c2 in the range of real numbers +-100 for c1 and c2 for each x, which combined give "...
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228
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Finding recurrence formulas from procedural code and output lists associated with integer sequences
This code outputs 37 sequences and takes about 15-minutes to run. I would like to be able to see how many and which variables { i, j, k, m, n } each of the 37 ...
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Return last number in sub-sequences in a list of integers
Given a list of integers like this:
z = {113, 117, 118, 119, 120, 121, 475, 476, 529, 538, 542, 543, 544}
I want a function that returns:
...
- 1,254
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117
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Integer sequence and RAM limits [closed]
I am trying to calculate the set of unique differences in a sequence, however the sequence grows fast and I hit the RAM limit of my PC for nthPrimeToUse = 11. For nthPrimeToUse 1 to 10 the output of ...
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Generate and graph the Recamán Sequence
I was surprised to see that we don't have any posts that mention the Recamán Sequence, so I figured I should post it as a challenge. By definition, $a_0=0$ and $a_n=a_{n-1}-n$ if the r.h.s. is ...
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RandomInteger with equal number of 1 and -1
I want to generate a list of random integers with only three values 1,0,-1. I know it can be done through RandomInteger[{-1, 1}, n]. How can I impose constraint on this list so that every integers in ...
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2
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127
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Mathematica analog to Wolfram|Alpha dataset analysis [closed]
I have a set of sequences with length 8,48,480,5760,.. and would like to do sequence analysis on them. I plugged the length 8 sequence into wolframalpha:
https://www.wolframalpha.com/input/?i=11,+2,+...
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Something is wrong with the implementation of the ThueMorse function
While trying to answer this Math.SE question, I believe I found several bugs in Mathematica and Alpha relating to the Thue-Morse sequence.
As a quick reminder, the $n^{\rm th}$ element of the Thue-...
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Find all integer tuples in a bounded region
For given rational numbers $p_1/q_1,p_2/q_2,p_3/q_3$ and a negative integer $d$, I'd like to find quadruples of integers $(w,x,y,z)$ in a rectangle(of particular sidelengths) satisfying the series of ...
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FindGeneratingFunction gives up too easily [closed]
I am trying to automatically find a generating function from the coefficients of a simple rational function using Mathematica's FindGeneratingFunction:
...
- 341
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1
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Constructing the following figure using mathematica
How do I construct the figure in the image using the formulae in Mathematica? I defined the following functions for the 4 cases. Can you also explain the significance of these in relation to the ...
user60670
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3
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How to construct rectangular figures from the Fibonacci numbers?
How do you construct rectangular figures ("golden rectangles") using the Fibonacci numbers in Mathematica using graphics? I know that the basis of the construction of these figures are the formulae ...
user60670
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1
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79
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How to postulate a formula for the following Mathematica function
I am using Mathematica to explore the properties of the Fibonacci Sequence. Below is the functions I have defined
...
3
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1
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93
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how to obtain these increasing integers for given n and m?
Let n and m be natural numbers. Then, how does one write a function ordint[n,m] that gives ...
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Guess Diophantine equation from its solutions
Take for example the equation
$$
n^2=x^2+y^2+1
$$
where $x,y$ are integers.
This equation admits solutions only for some values of $n$, to wit,
$$
n=1,3,9,17,19,33,35,51,73,81,99,\dots
$$
Can we ...
1
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1
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388
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Is there a way to exclude certain numbers in a sequence?
For example, the sequence of triangular numbers can be expressed as $1/2 [n (n + 1)]$ with $n=1,2,3,4,...$ but is it possible to create a summation of everything remaining $(2,4,5,7,8,9,11,12,13,14,......
- 11
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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, ...
- 1,121
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3
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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] == 1}, x[n], n]
Returns unevaluated ...
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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?
user47870
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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)
...
- 125
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451
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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 ?)...
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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 ...
- 297
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805
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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 $\{1,2,3,4,5,6,7,8,9,0\}$ (...
user52558