Questions tagged [integer-sequence]
The integer-sequence tag has no usage guidance.
110
questions
2
votes
2
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Recovering formulas for sequences with integer coefficients
Suppose I know the sequence is of the $a n^4 + b n^3 + c n^2 + d n$, with positive integers $a,b,c,d$, what is the easiest way to get them from the first few coefficients?
Here are the sequences I'm ...
- 8,135
20
votes
6
answers
826
views
Peaks, plateaus and ledges
I want to find the peaks, plateaus and ledges of an integer sequence, but all my attempts failed.
1. Example list
...
- 49.2k
5
votes
4
answers
181
views
Joining constant arrays determined by a subsequence of contiguous block of ones
I have the following:
data = {15, 25, 35, 45, 55, 65, 75, 85, 95, 105};
selector = {0, 1, 1, 0, 1, 1, 1, 0, 0, 0};
I want to create the following list from ...
9
votes
6
answers
1k
views
How can I define a sequence of Integers which only contains the first k integers, then doesnt contain the next j integers, and so on
I need a list of integers to check if a variable has one of the values of the list.
If[ MemberQ[List,x], Green, Red]
The list contains integers and is characterized ...
- 427
3
votes
1
answer
104
views
Enumeration of a certain sequence IV
Let $F_n$ denote the $n$-th Fibonacci number. I am interested in the sequence $$a(k, n)=\left | \left \{0 \leq m \leq n: \frac{F_m}{k} \; \text{is a perfect square} \right \} \right |,$$
where $|\...
- 75
0
votes
1
answer
41
views
Derivative with respect to a sequence
I want D[Subscript[a, k],Subscript[a,j]] to return something like the Kronecker delta. Is this possible?
-1
votes
4
answers
83
views
How to prove that 3(x) + y always results in a triangular number? [closed]
Assume that :
x = (n^2-n)/2
y = ((n+1)^2)-(n+1))/2
n is an integer and n ≥ 0
Examples =
3(0) + 1 = 1
3(1) + 3 = 6
3(3) + 6 = 15
and so on.
- 9
7
votes
1
answer
266
views
Recurrences related to Ramanujan's 1/pi formulas for level 10?
In the course of my research years ago, I came across three integer sequences related to Ramanujan's pi formulas but for level $10$. Their recurrence relations may be important. (Just like the level $...
- 437
1
vote
1
answer
54
views
Nested sequence evaluation seems to fail [closed]
I tried do define two OIES Sequences like that:
...
0
votes
0
answers
36
views
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 ...
- 5,187
5
votes
1
answer
303
views
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 ...
- 145
2
votes
5
answers
273
views
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
4
votes
0
answers
75
views
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 ...
- 1,943
3
votes
1
answer
62
views
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 ...
- 369
2
votes
1
answer
263
views
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 ...
- 369
3
votes
2
answers
131
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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
...
- 5,562
1
vote
0
answers
76
views
“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 ...
- 7,163
3
votes
0
answers
58
views
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 ...
- 763
2
votes
1
answer
162
views
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 ...
- 5,562
1
vote
1
answer
168
views
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
votes
1
answer
230
views
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?
...
11
votes
3
answers
2k
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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) $\bmod n$...
- 333
0
votes
1
answer
81
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 ...
- 522
3
votes
2
answers
149
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 ...
- 321
3
votes
2
answers
190
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.
...
- 1,941
1
vote
2
answers
148
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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{...
- 1,941
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votes
4
answers
586
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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?
- 67
1
vote
2
answers
125
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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:
...
- 199
3
votes
2
answers
78
views
How to sort Dataset where each row include a sequence of strings and integers
I got this type of data :
...
- 33
3
votes
1
answer
251
views
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 ...
- 483
2
votes
0
answers
82
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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 ...
- 983
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vote
1
answer
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7
votes
3
answers
220
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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
2
votes
1
answer
407
views
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 ...
- 23
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0
answers
104
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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
3
votes
2
answers
272
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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 "...
- 493
1
vote
1
answer
234
views
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 ...
- 493
8
votes
5
answers
346
views
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:
...
- 1,294
1
vote
0
answers
119
views
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 ...
- 493
22
votes
4
answers
1k
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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 ...
6
votes
4
answers
952
views
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 ...
- 677
2
votes
2
answers
128
views
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,+...
- 493
4
votes
1
answer
117
views
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-...
- 989
1
vote
0
answers
52
views
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 ...
- 111
3
votes
1
answer
83
views
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
2
votes
1
answer
203
views
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
12
votes
3
answers
1k
views
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
0
votes
1
answer
82
views
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
votes
1
answer
94
views
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 ...
- 255
3
votes
1
answer
110
views
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 ...