Questions tagged [sequence]

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

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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
130 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 ...
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2answers
141 views

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 ...
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2answers
61 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=\...
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2answers
197 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: ...
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3answers
418 views

Slow computation of recursive sequences

I want to investigate the asymptotic behavior of the following recursive system: ...
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0answers
42 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
31 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
84 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:...
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2answers
377 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 ...
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1answer
44 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 ...
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5answers
111 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 ...
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2answers
72 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 ...
3
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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: ...
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1answer
82 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? $\...
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2answers
147 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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3answers
432 views

Generate this sequence more efficiently

Is there a more effecient way to generate the sequence shown below. ...
5
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1answer
62 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
92 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
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1answer
93 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
29 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
59 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
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1answer
144 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
118 views

Generating Manipulate variables from a list of rules

I have the following list of rules: ...
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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[...
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2answers
64 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
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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
140 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
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4answers
173 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
60 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
91 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
234 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
71 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 ...
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0answers
75 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 ...
1
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1answer
116 views

Finding general formula for this recursion function

I have a recursion relation defined as ...
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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
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0answers
129 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
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1answer
56 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 ...
0
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1answer
113 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
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1answer
54 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
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2answers
115 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 ...
2
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3answers
122 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
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1answer
88 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
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0answers
85 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 ...
3
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1answer
108 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
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1answer
139 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
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1answer
105 views

Summing factors of binomial coefficients - get general formula?

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