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

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18
votes
0answers
312 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 ...
11
votes
4answers
764 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. ...
11
votes
2answers
254 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
293 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
1answer
449 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: ...
9
votes
5answers
404 views

Repeating Digits

I have written ...
7
votes
5answers
271 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
1answer
175 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
6
votes
5answers
238 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 ...
6
votes
1answer
89 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 ...
5
votes
5answers
3k views

How to detect if a sequence of integers is consecutive

I'm not a math-guy really (a programmer actually) and this is my first question. And excuse me if I can not explain my problem good. The problem is I have a sequence of integers and I want to detect ...
5
votes
1answer
172 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, ...
4
votes
5answers
342 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}\ ...
4
votes
3answers
208 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
128 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
569 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 ...
4
votes
0answers
69 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
96 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
2answers
118 views

Finding large Collatz Sequences, trying to improve speed

Background: I am already very much in love with Mathematica but I am also a novice. So far I have only gathered experience in procedural programming in Python. Generally speaking I am trying to ...
3
votes
3answers
118 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
243 views

Generation function of recurrence sequence

I'm trying to find generation function of recurrence sequence ...
3
votes
0answers
77 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
2answers
225 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
132 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
280 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
71 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
111 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
1answer
231 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 ...
2
votes
1answer
145 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
79 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
55 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
222 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
82 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
3answers
144 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
72 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
181 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
43 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 ...
1
vote
1answer
114 views

How to define Similarity Rules?

I have a question about Mathematica's SimilarityRules defining (for e.g. SequenceAlignment function). So help centre clearly ...
1
vote
1answer
99 views

sequence of matrix multiplications

My linear algebra book has questions that are are marked to use math software. There's probably some $50 guide on how to do everything but usually documentation has gotten me through. I've been kind ...
1
vote
1answer
54 views

Change input parameter order in a function

I'm a beginner in Mathematica programming and I'm trying to understand how input parameters work in Mathematica's function. I encountered a problem with the sequence/order of the input parameters of ...
1
vote
2answers
38 views

Imploying a sequence in a series

I would like to have the following sequence, $(a)_n$, in a series where $a_0 = 1$ and $a_n = a(a+1)\cdots (a+ n -1)$. The series I have is $$ 2\sum_{n=0}^{\infty}\frac{(1/2)_n}{n!(2n+1)^3} $$ I know ...
1
vote
1answer
148 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
1
vote
2answers
90 views

Number of sequences with a certain condition

Suppose I have the sequence {2, 4, 6, 8, 10, 12, 14, 16}. How could I calculate the number of tuples so that for every term save the first one, the difference from ...
1
vote
0answers
78 views

Find algorithm or generator formula with automated procedure and pattern recognition

I am trying to find a generator formula for the discriminant of a polynomial and believe it would be an interesting problem for the Mathematica community to know how to automate evaluation of certain ...
1
vote
1answer
70 views

How to Solve a Sequence in Mathematica [duplicate]

Given the input and the output, how do you interpolate a function in Mathematica? For example if you know that $f(1)=\frac{1}{2}$, $f(2)=\frac{1}{3}$, $f(3)=\frac{1}{4}$,... how would you solve for ...
1
vote
0answers
292 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
44 views

Compute an indefinite sequence of And

I would like to compute a condition of normalization over a set of vectors which has the form $$ (x_1.x_1 =1 ) \land ...\land (x_n.x_n=1) $$ Where the $x_i$ are vectors, and $n$ is a variable fixed at ...
0
votes
1answer
65 views

Single formula for this sequence [closed]

Consider the following sequence. 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8 We can express this sequence by (an) where an=n/2 when n is even and an=0 when n is odd. Find a single formula for an ...