Questions tagged [sequence]

Questions on specifying order in and splicing of lists, including use of Mathematica Sequence objects.

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11
votes
2answers
164 views

The use of SlotSequence in If[#1 > #2, ##] &

The below function when applied to a list of two elements, will output the maximum between the two: If[#1 > #2, ##] & For example: ...
4
votes
3answers
401 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
0
votes
0answers
32 views

How to convert a symbolic recursive formula to a non-recursive one

I am new to Mathematica. I want to convert a recursive formula to a non-recursive one using symbolic math. Specifically, I have a recursive formula similar to this: $a_n = f_a(c_{n-1}, x_{n-1})$ $...
1
vote
0answers
27 views

Is there a way to predict permutations that consist of sets?

SequencePredict is a function that predicts the next value from the arranged data. But I want to use the data for the combination to predict the next combination(...
1
vote
2answers
80 views

Short Normal Numbers in base 10

Normal numbers in base 10 are those for which, in the base 10 decimal expansion, you can find every natural number. Champernowne's number is a very simple example of this where it is simply written as:...
5
votes
2answers
373 views

Turning arguments into exponents

I'd like to replace every instance of L[stuff], e.g., L[-1,-2,-2] in an expression with ...
2
votes
1answer
41 views

SequenceReplace is incorrectly modifying the list when a pattern partially matches

(Below is a big simplification of my actual use-case which reproduces the problem with SequenceReplace. Please assume my use of ...
0
votes
0answers
73 views

Is there an integral number `k` satisfying the equation `a[n] = k^2`?

I have a sequence a[n] with $$a(n+1)=4 a(n)-2 a(n-1),\quad a(0) = 1,\ a(1) = 28.$$ I use ...
3
votes
5answers
105 views

How to rearrange the terms in polynomials to the power of x?

Here is my code Eliminate[y == x + n && x^2/6 + y^2/3 == 1, y] I got 6 - 3 x^2 == 2 n^2 + 4 n x But I wanna it to be ...
1
vote
2answers
64 views

Computing recursive sequence [duplicate]

I would like to compute a[1000] of the following recursive sequence a[1] = 1; a[n_] := a[n - 1] + 1/a[n - 1]^2 but it takes a long time for computing even small ...
4
votes
4answers
1k views

How to get Mathematica to show limit of a recurrence sequence?

I want to find the limit of a such a sequence: $f(n+1)=\sqrt{2f(n)-1}, \, f(0)=a, a>1$ How does one do this? Is it possible to have it show the solution algebraically, like it does with ...
3
votes
1answer
62 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: ...
1
vote
2answers
114 views

How to define a recursive sequence

I would appreciate if somebody could help me with the following problem: Q: How to define this in Mathematica. $$a_{n+1}=\begin{cases} a_{n} & ,a_{n} \ge n\\ 2n-a_{n}& ,a_n<n \end{cases}...
0
votes
1answer
77 views

Finding a sequence with RecurrenceTable

I would appreciate if somebody could help me with the following problem: Q: How can the following recursion equations be solved using RecurrenceTable? $\...
4
votes
3answers
431 views

Generate this sequence more efficiently

Is there a more effecient way to generate the sequence shown below. ...
5
votes
1answer
60 views

How to set up patterns when using SequenceSplit

Given a list lst={0,0,0,0,0,"A1",0,0,0,"B2",0,0,"C3","D4","E5",0,0,0,"F6"} How to split it as ...
0
votes
1answer
85 views

Convert a piecewise definition of a single impulse into an impulse train

NOTE: See update at end of question I have a function smoothstep (based on the derivative of a smoothstep function) that gives a single impulse as follows: ...
4
votes
1answer
78 views

Longest Repeated Substring

Is there a solution in Mathematica to the problem of finding the longest substring of a sequence that occurs at least twice.For example {1, 2, 3, 4, 5, 2, 3} has ...
1
vote
1answer
28 views

Splitting a list of letters into subsequences starting with uppercase letters [duplicate]

Given a list of upper/lowercase characters, I'm trying to split it into subsequences that start with an uppercase and contain the next few (not necessarily positive number of) elements up until the ...
2
votes
2answers
55 views

Counting the number of Configurations in an Array with Constraints

Consider an array $$\{a_i\}, i=1, ..., N$$ with periodic boundary condition, i.e. $i\equiv i+N$. $a_i\in \{0, 1\}$. I would like to count the number of configurations of the array $\{a_i\}$ satisfying ...
5
votes
1answer
136 views

How to find the length of an indefinitely repeated sequence in a list

Here, I am not looking for simply a repeated element, but an indefinitely repeated sequence. For example, if I have the list ...
2
votes
1answer
108 views

Generating Manipulate variables from a list of rules

I have the following list of rules: ...
3
votes
2answers
84 views

How to convert the solution of this recurrence like this form?

I am trying to solve the recurrence sequence. I tried RSolve[{a[n] == 1/2 (a[n - 1] + 9/a[n - 1]), a[1] == 1}, a[n], n] // Simplify I got {{a[n] -> 3 Coth[...
-1
votes
2answers
61 views

Please help me get the ratio of x to y [closed]

I need the ratio of x to y in this equation: sum [n*(x/10)^n/10^(n-2)] == y from n=1 to ∞ Thank you!
2
votes
1answer
49 views

Define a variable whose value for each i in [|1,n|] depends on the average value it takes for j different from i [closed]

I would like to define the following variable : So the average value (a) takes for every "individual" but i. But actually, for each i, the value (a) takes depends on the preceding average: ...
3
votes
1answer
137 views

Taking a long time to produce output

In the following, I want to know b[1000], but it is taking a very long time even for b[30]. Please help ...
2
votes
3answers
78 views

Function of a function, both of a list of variables

I am trying to avoid dealing with long explicit lists of variables. What i do so far is the following: VarList={x_, y_}; ParList={x, y}; ValList={2, 3}; What ...
3
votes
4answers
172 views

@ and Sequence ( and /@ ) [duplicate]

list = { {a,b}, {c,d}, {e,g} } How to efficiently get { f[a,b], f[c,d], f[e,g] } I tried various combinations using ...
1
vote
1answer
55 views

Weird Behavior of Table and Sequence

I'm writing a function that constructs a multidimensional array (that is, nested lists) using Table. The dimension of the array varies according to the argument to ...
3
votes
1answer
86 views

When does Slot evaluate?

I looked up the related answers, it must have to do with the scope. Toy example similar to mine in structure: ...
2
votes
1answer
207 views

Find Sequence Function Error?

I am suprised that mathematica is not able to find the function for the following sequence: ...
1
vote
1answer
70 views

Extracting blocks of “adjacent” XMLElements

I have a file that, when imported as an "XMLObject", returns an XML object that possesses this general structure: (I've stripped the inconsequential junk wrapping ...
1
vote
0answers
70 views

Possible bug with `FindSequenceFunction`$.$

Consider the following code: g = Table[Sign[StieltjesGamma[n]], {n, 0, 30}]; s = FindSequenceFunction[g]; The result is a certain ...
10
votes
7answers
687 views

Counting subsequences (i.e., patterns) within a list?

I would like to count the number of subsequences in list. Say I have data given by: data = {1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1}; I would like to count the number ...
1
vote
1answer
116 views

Finding general formula for this recursion function

I have a recursion relation defined as ...
1
vote
0answers
59 views

Speed up for SequencePredictorFunction?

From Google Dive: SequencePredictorFunction is here, along with my test data. From pastbin: prediction function and data is here. Using the ...
2
votes
0answers
101 views

Find the second longest common subsequence?

I am trying to determine that how my sequence(probe) "hits" against a long sequence(genome). The LongestCommonSubsequence in Mathematica gives the first longest common subsequence between two ...
2
votes
1answer
54 views

How can I create a sequence of solutions to an equation?

I'm brand new to Mathematica and having to use it for my PDE class. One of my homework questions involves plotting the first few terms of the Fourier series of a solution to a PDE, but the eigenvalues ...
4
votes
4answers
1k views

Limit of sequence

I tried to calculate the following limit $$\lim_{n\to\infty}n\sin(2\pi en!)$$ Mathematica gets ...
0
votes
1answer
100 views

Sum of Sequence inside a replace rule? [duplicate]

I'd like a replacement rule that replaces derivatives with their total order. I tried ReplaceAll[Derivative[x__] -> Plus[x]][Derivative[1, 1]] but it doesn't ...
0
votes
1answer
51 views

FindSequenceFunction applied to basic trig sequence

I an not too familiar with FindSequenceFunction. Is there a trick to make Mathematica produce the obvious sequence function for this sequence? Example 1 ...
2
votes
2answers
114 views

Alternatives to Sequence[] as a nonexistent expression element [duplicate]

I stumbled upon this code by Leonid Shifrin. He uses Sequence[] to create void or non-existent output. I was wondering whether this is really the best way to ...
14
votes
1answer
211 views

Pattern matching with List and Optional

Bug introduced in 8.0.4 or earlier and persists through 11.1.1 Thank you for bringing this to our attention. I have filed a report with our developers. Why does this ...
2
votes
3answers
115 views

How can I implement the binomial transform?

How do I implement the binomial transform? I've tried defining a matrix P = Table[(-1)^k Binomial[n, k], {n, 0, m}, {k, 0, m}] and having this act on my ...
0
votes
1answer
84 views

Is there a simple way to convert a list to a sequence? [closed]

I have a list of couples like this for example : list = {{1, 2}, {2, 3}} In practice my list can be of any size. I need to put a condition in ...
0
votes
0answers
82 views

Is there a **simple** way to define a function on a variable sequence?

I have a List j={j[1],j[3],j[6]}. But this list is in fact a variable of my code, so i could have j={j[6],j[10]} either. I need ...
10
votes
3answers
459 views

How to implement symbolic Ramanujan's summation in Mathematica?

How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...
3
votes
1answer
105 views

Hazrat Exercise 9.2: Sequence resolves to Factorial?

Throwaway comment in Hazrat p105: Observe that Range[10]/.{x_,y___}->y/x amounts to 10! I can't for the life of me figure out how this works. It seems to ...
1
vote
1answer
129 views

Constructing a list of all three-element subset of a list [closed]

The list I have is {a,b,c,d,e} I would like to use ReplaceList to construct a list of three-element subset of the above list. ...
4
votes
1answer
102 views

Summing factors of binomial coefficients - get general formula?

Consider summing more and more factors of binomial coefficients: ...