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

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25
votes
0answers
573 views

Performance problems in new Sequence functions

The new-in-10.1 Sequence* family of functions should provide newly optimized methods for handling sequence problems. Happily in some cases they do! For example ...
15
votes
2answers
1k views

What happens when you divide by ##?

I've been playing around with sequences a bit. In particular with using ## with unary and binary operators. Let's start simple, the following all make some kind of ...
13
votes
4answers
901 views

How can I return a Sequence?

Recently I had the need to redefine a certain symbol in my init.m so it would be automatically omitted from any lists it appears in. I decided to redefine it to an empty sequence, e.g. ...
12
votes
2answers
238 views

Unexpected behavior of Sequence — using Sequence to delete parts of an expression

I thought that assigning Sequence[] to the part of an expression was an effective way to remove it. For example, the following code yields {2,3,4,5}: ...
11
votes
2answers
294 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 ...
11
votes
1answer
307 views

Empty Blank regression in v10.1

Bug introduced in 10.1 and fixed in 10.2.0 In v10.1.0.0 on Linux, when Blank[] is used in Alternatives with pattern that can ...
10
votes
5answers
425 views

Repeating Digits

I have written ...
10
votes
1answer
559 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
8
votes
9answers
366 views

Positions of elements in the initial flattened list in a split list

Say, we have a list: m1 = {2, 2, 7, 0, 7, 7, 2, 2, 2} It can be split easily: ...
8
votes
5answers
341 views

How can I tally continuous sequences in a list?

I have a stream of data like this: 0001100111100000111111001110000001111111111000000111000111110000... (I can represent them as a list, like in {0,0,0,1,1,...}, ...
7
votes
5answers
327 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 ...
7
votes
1answer
241 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
7
votes
2answers
136 views

`FindSequenceFunction` for sum of hypergeometric terms?

The built-in function FindSequenceFunction is quite good at recognizing hypergeometric terms, i.e. terms $c_k$ for which $c_{k+1}/c_k$ is a rational function of $k$....
6
votes
3answers
355 views

Match a sequence of integers

I would to match a pattern p1 = 0,0,1,0,0 to the elements in listA. The elements are a boolean sequence that may look like this ...
6
votes
1answer
102 views

Find subsequence A in sequence B A007908 - OEIS

I have sequence A as A007908 - OEIS and pattern B which is a sub-sequence of that sequence A. I need to find index of first occurrence of the given pattern. For example pattern ..1010... I've looked ...
5
votes
1answer
84 views

An unexpected match when using Condition, Optional and passing a Sequence

Mathematica is behaving in an expected way when passing a parameter with an Optional and a Sequence. Here is an example: ...
5
votes
2answers
1k views

How to find a recurrence relation for a numerical sequence?

This question was inspired by Vladimir Reshetnikov's question (How to find a recurrence relation for a sequence?): Given a finite sequence of numbers, how can we find in MMA a recurrence relation ...
5
votes
1answer
202 views

Find the domain in which a sequence converges

I seem to have a lot of problems in the format of: Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges. However, ...
5
votes
0answers
57 views

SimilarityRules for SequenceAlignment of two lists

I am trying to use the SimilarityRules option of SequenceAlignment to customize its output. This works perfectly for strings, ...
4
votes
5answers
370 views

Sequence generation

If I wanted to generate a sequence that follows the pattern $$x_{n}=x_{n-1}+\dfrac{1}{2}\left(\sqrt{1-y_{n-1}\ ^{2}}-x_{n-1}\right)\\ y_{n}=y_{n-1}+\dfrac{1}{2}\left(\sqrt{1-x_{n}\ ^{2}}-y_{n-1}\...
4
votes
3answers
225 views

Limit n->Infinity of recursive sequence

I have defined a recursive sequence a[0] := 1 a[n_] := Sqrt[3] + 1/2 a[n - 1] because I want to calculate the Limit for this ...
4
votes
3answers
239 views

Long waiting time for computing a summation

It takes a long time to compute the summation below, and I'd like to know if there are alternative ways to compute things faster. When replacing $15$ by $\infty$, then I should get $3^{1/3}$. I need ...
4
votes
2answers
142 views

How can I use sequence in plotting domain?

I would like to plot a function but have a domain defined elsewhere as follows: xrange = Sequence[0, 2π]; Plot[Sin[x], {x, xrange}] However, this doesn't work ...
4
votes
2answers
220 views
4
votes
0answers
38 views

Pattern match Shortest BlankNullSequence in SequencePosition

Apologies if this has an answer somewhere but I can't find it. From the examples for SequencePosition we are shown that ...
4
votes
0answers
84 views

Does it help to do any preprocessing before `FindSequenceFunction`?

I am always amazed how smart FindSequenceFunction can be in discovering general term formula for a sequence of rational numbers. The documentation says it can work ...
3
votes
2answers
122 views

How to deduce the Ramanujan's summation of this series?

I have already asked a similar question about Ramanujan's summation in general but received no good answers. Now I am interested in this exact series: $$\sum _{n\ge1}^\Re (24 n + 12 n^2)$$
3
votes
3answers
164 views

Tangled up in sequences and recurrence relations

I took a trip through sequences and recurrence relations and I got tangled up since the documentation didn't help much. I'm sure you can. Given a sequence ...
3
votes
2answers
80 views

Generating a sequence of lists [closed]

I have learnt how to generate a sequence of numbers, but now I come across a question whether it is possible to generate e sequence of lists. Say, I would like to generate {1},{1,2},{1,2,3},...,{1,2,3,...
3
votes
3answers
118 views

How can I make custom accumulated sequences like the following?

First of all, I don't really know how to formulate the question, so if you understand my question and know a better way to phrase it, please revise. I have the following Matrixes: ...
3
votes
2answers
321 views

Generation function of recurrence sequence

I'm trying to find generation function of recurrence sequence ...
3
votes
0answers
84 views

How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
2
votes
3answers
95 views

Using a piecewise defined sequence, find all $x_0$

Given $0\le x_0<1$, let $$x_n=\begin{cases} 2x_{n-1}, & \text{if $2x_{n-1}<1$}\\ 2x_{n-1}-1, & \text{if $2x_{n-1}\ge 1$} \end{cases}$$ for all integers $n>0$. For how many $x_0$ is ...
2
votes
2answers
251 views

Defining a sequence slot programmatically

This question is related to: Composition of functions using slots `Slot` (#) interfering with evaluation Consider a toy example: ...
2
votes
3answers
142 views

Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
2
votes
1answer
337 views

how can I solve integrals including recursion of some sequences of functions

I would like to solve the equations as given below in mathematica. I have written some codes before but I have no idea when there is sub indexing to indicate the series of functions. I will be very ...
2
votes
1answer
74 views

Matching a list of sequences with common form

I am trying to find a pattern that matches a list of sequences that share a common form. The sequence form is: 1 followed by zero or more nonzero integers, followed by 0. An example list is: ...
2
votes
2answers
41 views

Find the Kimberling Sequence

How to find the Kimberling Sequence by using Mathematica? each row is obtained from the previous by boxing (and expelling) the main diagonal element, and then reading the first number after the ...
2
votes
2answers
119 views

Problem on Consecutive Sequence Sums that are Squares

Here is a seemingly simple Problem: I have two natural numbers n and m, n < m such that S1:= n +...+ m is a square and also S2:= n +...+ m + (m+1) is a square. Problem a) : Find n and m. You ...
2
votes
2answers
548 views

Limit of sequence

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

Generating a list of specific intermediate numbers associated with continued fractions

First of all, I don't know how ContinuedFraction[] or Convergents[] are implemeneted, and I think it is immaterial to my ...
2
votes
1answer
90 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
2
votes
0answers
58 views

pattern matching and applying a function, not working as expected [duplicate]

Consider the following code G[x, y] /. a_[b__] -> Total[a @@@ Permutations[List[b]]] I expect it to give G[x, y]+G[y,x] ...
2
votes
0answers
278 views

Faster Ways to compute recursive summation

It takes a long time to compute the summation below, and I'd like to know if there are some better ways to compute things faster. I have used $3$ ways to calculate, but they are very unsatisfactory. I ...
2
votes
0answers
84 views

Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity]

I would like to show that the following (and other similar formulae) tends to zero. Limit[Sum[(2*E*n)^w/(w^(n/2+w)), {w,2,n}],n->Infinity] What's the right ...
1
vote
4answers
337 views

Find a sequence given the sums of its terms

For a certain sequence of numbers, the sum of the first $n$ numbers in the sequence is given by $n^3+4n$ for all positive integers $n$. What is the fifteenth number in the sequence? How do you solve ...
1
vote
3answers
272 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 ...
1
vote
2answers
74 views

Plotting non-linear recursive sequence

I'm a total noob with Mathematica, and while trying to plot the following, I get several error messages. What am I doing wrong? ...
1
vote
1answer
209 views

Defining a recursive integral sequence

I have a recursive integral sequence as follows: $$y_0(x)=1+r,$$ $$y_1(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_0(t) dt,$$ $$\vdots$$ $$y_n(x)=-\frac{1}{\Gamma(a)}\int_0^x (x-t)^{a-1} y_{n-1}(t) ...
1
vote
1answer
48 views

Sequence not working in Manipulate?

I have a function that I would like to construct the Manipulate parameter list with Sequence. This is a simpler example but it ...