Questions tagged [sequence]

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

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0answers
57 views

Avoiding the memory requirements of an accumulation of returned Nulls (etc)

There is an extensive but relatively old answer to a similar question here, and there are many Qs and As about avoiding using Table where possible. My problem is a mixture of the two: I have been ...
3
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2answers
94 views

Generate a sequence of sequences

Imagine I have a sequence of M integers each of which is either zero or one. How do I generate a sequence of all such 2^M sequences?
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2answers
119 views

How to use a general method to solve this problem

Suppose $a_{n}>0(n=1,2,\cdots)$. The series $ \sum_{n=1}^{\infty} a_{n}$ converges and the constant $ \lambda \in\left(0, \frac{\pi}{2}\right)$. Now I need to judge whether the series $\sum_{n=1}^{\...
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2answers
161 views

How to judge whether the series is absolutely convergent?

I need to judge whether the series $\sum_{n=1}^{\infty}(-1)^{n}\left(1-\cos \frac{\alpha}{n}\right)$ (α>0) is absolutely convergent. ...
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3answers
68 views

How to find the limit of this recursive sequence

I want to find the limit of the following recursive sequence when n tends to : ...
5
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2answers
134 views

How do I replace specific sequences of a sublist without changing the level of the list?

Suppose I have a list of multiple sublists: testlist={{1,1,1,0,0,0,1,1,1,0,1,1},{1,0,0,1,1,1,1,0,1,1,1,0}} I want to replace given sequences without creating new ...
4
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1answer
248 views

What does Sequence[2,4]^2 mean?

I am learning pattern matching. An example that confuse me is as follows. Foo[x__?EvenQ] := x^2; Foo[2, 4] which is equal to ...
5
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1answer
71 views

head of a sequence

Why does Head[Sequence[b, c]] return c[Symbol] and not Sequence? Why does ...
2
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1answer
46 views

Splice matching function arguments

Mathematica 12.1 introduces Splice that replaces the old way of using Sequence@@ to "melt" a list of entries. However, the ...
0
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1answer
35 views

Plot any parametrization (pure function, numbered variables)

I'd like to write a function plot[reg_,f_] that takes as input any product of intervals (list of pairs of reals) reg$\subseteq\!\...
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0answers
28 views

Pattern matching on derivatives

I want to manipulate and do pattern matching on sequences of functions and their derivatives, but I'm struggling to work with the multiple indexing required. Here is an example. Let $$ y(z) = \sum_{j=...
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0answers
37 views

Apply SequenceReplace with a fixed shift

How can I apply SequenceReplace with a fixed prespecified shift instead of a shift equal to the length of the pattern, on a given list? E.g. ...
6
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2answers
238 views

Build general form of an infinite sequence

Please, I would like to build the general form of an infinite number sequence $$\dfrac{8}{35}, \dfrac{5}{21} ,\dfrac{8}{33} ,\dfrac{35}{143},\dfrac{16}{65} ,\dfrac{21}{85} ,\dfrac{80}{323},\...
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0answers
59 views

FindSequenceFunction instantly throws an exception

FindSequenceFunction[{2, 4, 6, 7, 14, 29, 18, 5, 5, 2, 4}] SystemException["MemoryAllocationFailure"] $Version "12.0.0 ...
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0answers
147 views

How can I prevent errors with ReplicateLayer[]?

I am trying to build a NetGraph[] that takes input of the form {{0.6},{0.6},...,{0.8},{0.8}} and multiplies the last sequence ...
2
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2answers
67 views

Select subsets from a list based on a criterion?

Assume we have a set of numbers, for instance $A=\{2,3,4,5,6,7,8,9,10\}$ and we are looking for the sums of reciprocals such that they are less than one. I mean I am looking for all $S_B$'s $$ S_B=\...
11
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2answers
203 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
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3answers
433 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
0
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0answers
59 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: $a_n = f_a(c_{n-1}, x_{n-1})$ $...
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0answers
48 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
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2answers
89 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
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2answers
381 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
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1answer
52 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 ...
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0answers
75 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
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5answers
118 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
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2answers
84 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
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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
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1answer
64 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
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2answers
228 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}...
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1answer
84 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
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3answers
435 views

Generate this sequence more efficiently

Is there a more effecient way to generate the sequence shown below. ...
5
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1answer
66 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
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1answer
116 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
123 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
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1answer
35 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
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2answers
63 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
155 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
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1answer
138 views

Generating Manipulate variables from a list of rules

I have the following list of rules: ...
3
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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
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2answers
68 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
56 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
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1answer
142 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
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3answers
81 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
177 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
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1answer
70 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
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1answer
102 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
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1answer
281 views

Find Sequence Function Error?

I am suprised that mathematica is not able to find the function for the following sequence: ...
1
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1answer
72 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
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0answers
81 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 ...