The utilization of advanced computing technology in mathematical research: new mathematical results discovered partly or entirely with the aid of computer-based tools.

learn more… | top users | synonyms

1
vote
1answer
42 views

Complicated probability question [closed]

There are 20 empty present boxes numbered from 1 to 20 are placed on a shelf, there are 4 men standing in front of the shelf. Each one asked to pick in his mind 3 numbers without telling any one then ...
0
votes
5answers
92 views

Can we prove that plumb line is vertical to ground?

Using a plumb line to make sure a wall is vertical for instance, is as far as I know one of the most primary tools in the sense that the very-very ancient builders used it as an instrument. I was ...
0
votes
0answers
15 views

stochastic experiments like galton board?

do you know some other stochastic/statistic experiments like galton board? I'm looking for something that could be build for learners or people who are interested in mathematics; some sort of "...
1
vote
0answers
27 views

Assigning levels in factorial design.

I am sorry if the question is too basic. Actually while doing some experiment on 2-level factorial design, I assigned +1 to a low level and -1 to high level. I just need the sign of the regression ...
0
votes
1answer
34 views

A computational experiment about identities involving the sum of remainders function

Let $\sigma(m)$ the sum of divisors function and $$S(m)=\sum_{k=1}^m\text{m mod k}$$ the sum of remainders function, then it is know that for integers $m>1$ $$\sigma(m)+S(m)=S(m-1)+2m-1.$$ On the ...
0
votes
0answers
3 views

Hypothesis testing: 2 groups with 2 subgroup each. Which test to use?

I recorded the pumping rate (measurement variable) of two types of worm: normal and mutant, with n=6 the number of worms per type. Then, I exposed these types of worms to a drug. BUT I used a ...
0
votes
1answer
25 views

Method to study obvious properties

Most of the time studying mathematics we come across various properties like associative, commutative,...etc. These properties are obvious and sometimes I feel why at all they are given in the text. ...
0
votes
0answers
21 views

how to logically modify a variable so that it accurately fits a given curve

I have 2 sets of experimental data. Each set has 2 variables (A,B) and response data (C). A1 100 100 100 100 100 100 100 B1 11.3 10.1 8.9 8.1 7.7 6.5 5.3 A1/B1 8.8 9.9 11.2 12.3 13.0 ...
4
votes
1answer
174 views

What subfields use computers the most and least? (soft question)

What areas within research mathematics use computer programming (not including $\LaTeX$) the most and least? What programming languages are most commonly used in those fields?
0
votes
0answers
23 views

How to calculate these particular values in this experiment?

I am running a statistics experiment where I need to calculate certain values. However, this is where I am having difficulty. Here is how the experiment works: Two Individuals Participate There is ...
18
votes
2answers
454 views

Most wanted reproducible results in computational algebra

I am interested in suggestions for major computational results obtained with the help of mathematical software but not easily verifiable using computers. "Most wanted" could refer, for example, to ...
16
votes
2answers
371 views

Conjecture ${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-\frac1{\left(e^x-1\right)x^3}\right]dx=\frac{\zeta(3)}{8\pi^2}$

I encountered the following integral and numerical approximations tentatively suggest that it might have a simple closed form: $${\large\int}_0^\infty\left[\frac1{x^4}-\frac1{2x^3}+\frac1{12\,x^2}-...
10
votes
1answer
105 views

Relationship between primes and practical numbers

This is my first post here. I am a musician, and not a mathematician, but I enjoy doing things to prime numbers and seeing what comes out. I have defined a sequence which takes the following values ...
0
votes
0answers
37 views

Guesstimating a probability distribution from plots, tails and moments

While working on a recreational / experimental math problem I have simulated some data and would like to find out the underlying distribution. For the moment I will consider the process which led to ...
12
votes
1answer
278 views

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

I was experimenting with hypergeometric-like series and discovered the following conjecture (so far confirmed by more than $5000$ decimal digits): $$\sum_{n=0}^\infty\frac{\Gamma\!\left(n+\tfrac14\...
23
votes
2answers
424 views

Conjecture $\int_0^1\ln\ln\left(\frac{1+x}{1-x}\right)\frac{\ln x}{1-x^2}\,dx\stackrel?=\frac{\pi^2}{24}\,\ln\left(\frac{A^{36}}{16\,\pi^3}\right)$

I did some numeric experiments with integrals involving double logarithms (because they received much interest both on this site and in published papers, sometimes under names of Malmsten—Vardi&...
1
vote
1answer
45 views

For $n\geq 1$, $\sum_{k=0}^{\infty}\frac{(-1)^{k}(nk+1)^{3}}{(k+1)^6}$ in terms of $\zeta(3)$ and $\zeta(5)$ from a series calculator. Is possible?

I am doing experiments with this widget (Wolfram Alpha, a Series calculator, by HIghOPS) http://www.wolframalpha.com/widgets/view.jsp?id=86ceba9f35c96ebae137e44a36c7261a and take for Example. ...
6
votes
0answers
91 views

Trilogarithm $\operatorname{Li}_3(z)$ and the imaginary golden ratio $i\,\phi$

I experimentally discovered the following conjectures: $$\Re\Big[1800\operatorname{Li}_3(i\,\phi)-24\operatorname{Li}_3\left(i\,\phi^5\right)\Big]\stackrel{\color{gray}?}=100\ln^3\phi-47\,\pi^2\ln\phi-...
5
votes
1answer
168 views

Please, help to identify this numerical constant

I'm trying to find an answer to this question. Let $K(k)$ be the elliptic integral of the first kind and $K'=K(\sqrt{1-k^2})$. According to Abel's theorem (see this link) we know that if $\frac{K'}{K}...
3
votes
1answer
54 views

Hints to compute if exists $\lim_{n\to\infty}\sum_{k=1}^n\sigma(k^2)/\sum_{k=1}^n\sigma(k)$, which $\sigma(n)=\sum_{d\mid n}d$, and other question

I would like receive hints at least for one of the following problems, these are going from experiments. Can you provide to me hints for at least one of the following problems? I will try put the ...
1
vote
2answers
39 views

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

Denoting as $$s(n)=\sum_{k=1}^n n \bmod k$$ the sum of remainders function (each remainder is defined as in the euclidean division of integers $n\geq 1$ and $k$). See [1] for example. For examples $...
1
vote
1answer
62 views

If $n$ satisfies $\left(-3+\sqrt{1+8n}\right)\sigma(n)=4\left(-1+\sqrt{1+8n}\right)\phi(n)$ then is an even perfect number?

Let an integer $m\geq 1$, and $\sigma(m)$ is the sum of positive divisors function, and $\phi(m)$ is Euler's totient function, counting the number of integers $1\leq k\leq m$ such that $gcd(k,m)=1$ (...
2
votes
0answers
45 views

With $rad(N)=\prod_{p|N}p$, if $N$ is even and $\frac{2+rad(N)}{8}\left(\sum_{\substack{d|N,d<rad(N)}}d\right)=N$ then is perfect?

In the literature (see for example sites and paper concerning to the abc conjecture, I say this as reference and by caution to avoid mistakes) is defined the arithmetical function $rad(n)$ as $1$ if $...
2
votes
2answers
28 views

On $\sigma(n)<n+\frac{n}{2}\log\frac{n+1}{n-1}+\frac{n}{4} \left(\sum_{\substack{d|n,1<d<n}}\log\frac{(n+d)(n+1)}{(n-d)(n-1)}\right)$

I've derived for $n>1$ and $\sigma(n)$ the sum of divisor function $\sum_{d|n}d$ the following inequality $$\sigma(n)<n+\frac{n}{2}\log\frac{n+1}{n-1}+\frac{n}{4} \left(\sum_{\substack{d|n,1<...
6
votes
0answers
120 views

Limit superior, limit inferior and a series involging $\sum_{k\nmid n}$k, where $1\leq k\leq n$

The purpose of this post is state assertions by the use of statements and hypothesis in an expository way and after I am asking for reasonable unconditionally results that you can provide us. Using ...
11
votes
2answers
247 views

Conjectured closed form for $\operatorname{Li}_2\!\left(\sqrt{2-\sqrt3}\cdot e^{i\pi/12}\right)$

There are few known closed form for values of the dilogarithm at specific points. Sometimes only the real part or only the imaginary part of the value is known, or a relation between several different ...
0
votes
1answer
47 views

Is this infinite product for zeta(2) trivial?

I have crafted an infinite product for zeta(2) shown here. Euler's prime product is the only one I'm aware of. In checking Math World, I don't see any products. Is that because they are trivial?
11
votes
1answer
242 views

Fibonacci numbers and the nontrivial zeros of the Riemann zeta function

Is this a mathematical coincidence? For $n=1,\dots,7$: $$ \left\lfloor \prod_{k=1}^n \arg\left(\rho_k\right)\right\rfloor = F_{n+1}, $$ where $\arg$ is the complex argument, $\rho_n$ is the $n$th ...
4
votes
1answer
60 views

Any correlation to Merten's function?

Here is a plot of partial sums of Liouville Lambda and Moebius Mu: Notice the differences (in green) are tantalizingly close to $-n^{\frac{1}{2}}$. Does this have any correlation to Merten's ...
0
votes
0answers
48 views

Can these steps be converted to a mathematical expression using equations/graph theory/Calculus/Set theory/functions/?

Want to convert below algorithm into a mathematical model:- General points 1. Let there be a Connected Directed Graph. G = (V, E) V vertices or nodes E edges. This graph can be seen as a network ...
-3
votes
1answer
338 views

On a 50 question multiple choice exam with 5 choices per questions, What are the odds that I get 100% if I were to Guess every answer? [closed]

What would the odds be to get 100% on a multiple choice exam where I guessed the answer to all 50 of the multiple choice questions (5 choices per questions)? A 1 in how many chance?
89
votes
9answers
16k views

If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin?

Consider a two-sided coin. If I flip it $1000$ times and it lands heads up for each flip, what is the probability that the coin is unfair, and how do we quantify that if it is unfair? Furthermore, ...
3
votes
1answer
84 views

Estimate number of songs a radio station has [duplicate]

Imagine the following problem: You listen to a radio station and take notes how often was each song played. How can you estimate based on your notes (e.g. 30 songs played once, 2 played twice, one ...
1
vote
0answers
38 views

Estimating the size of my population

I have a following problem: Imagine you have a hat with many different balls in it and you want to estimate, how many balls are totally in the hat. The only think you are allowed to do is to take one ...
7
votes
1answer
111 views

How to find this number, which is probably a very big prime or a product of big primes?

Let $\mathcal{N}(n)$ be the next prime greater than $n$. Which is the smallest natural number $n>0\;$ such that: $\mathcal N(2\cdot 3\cdot 5\cdot 7\cdot 11\cdot n)−2\cdot 3\cdot 5\cdot 7\cdot ...
11
votes
2answers
310 views

Yet another conjecture about primes

Let $\mathcal{N}(n)$ be the next prime greater than $n$. Conjecture: $\mathcal{N}(n!)-n!\:$ is either $1$ or a prime. It holds for n=1 to 99 and the expression is 1 for 3,11,27,37,41,73,77 and ...
0
votes
2answers
173 views

Balanced Latin Square

For making a good Between-Object user study, this is suggested to use a Latin Square to give all the different conditions, ...
1
vote
0answers
69 views

Sublists Conjecture

The conjecture: For those $k$ that have a saturated sublist $a_{j}$, the first occurrence is: $$j \geq k+3.$$ A proof will imply Oppermann and will be a start to a pattern-based attack on the ...
0
votes
2answers
82 views

Can a simple plot be used as a proof-without-words?

Can this simple plot be used as a proof-without-words? Edit "No, it suggests but does not prove." Plot of $2^{1 + n} = 1 + 3^n:$ Motivated by this question, I reworked the non-loopback ...
1
vote
1answer
44 views

Why the imaginary half circles is this plot?

I plotted the square roots of the Oppermann boundaries and got this: Why the imaginary half circles?
1
vote
0answers
66 views

Lower bounds on possible integer relations from the PSLQ algorithm

For the equation: $$ \sum_{i=1}^na_ix_i=0 $$ where all $x_i$ are real numbers and all $a_i$ are integers, the PSLQ algorithm can either find an integer relation or give lower bounds on the norm of ...
28
votes
2answers
492 views

A number $n$ which is the sum of all numbers $k$ with $\sigma(k)=n$?

For a positive integer $n$, let us define a set $$A_n = \{ k\in\mathbb{N} \mid \sigma(k) = n \}$$ where $\sigma$ is the divisor-sum function (a well-known multiplicative number-theoretic function). ...
59
votes
3answers
696 views

Closed form solution for $\sum_{n=1}^\infty\frac{1}{1+\frac{n^2}{1+\frac{1}{\stackrel{\ddots}{1+\frac{1}{1+n^2}}}}}$.

Let $$ \text{S}_k = \sum_{n=1}^\infty\cfrac{1}{1+\cfrac{n^2}{1+\cfrac{1}{\ddots1+\cfrac{1}{1+n^2}}}},\quad\text{$k$ rows in the continued fraction} $$ So for example, the terms of the sum $\text{S}_6$ ...
2
votes
1answer
424 views

Proof of Andrica when Assuming Oppermann

Proof of Andrica's conjecture by assuming Oppermann's conjecture. Oppermann's conjecture: $$n\geq2\wedge\pi\left(n^{2}-n\right) < \pi\left(n^{2}\right) < \pi\left(n^{2}+n\right).$$ Andrica'...
2
votes
1answer
109 views

How to test that this 3D graph is rigid?

I have constructed a lattice as a 3D graph while ensuring that it is rigid. I would like to find a way to test it to verify. Any thoughts? Links to papers?
14
votes
1answer
218 views

Websites that promote co-operation and social networking among mathematicians

Are there some websites that could be defined as social networks for mathematicians and scientists? What I have in mind is something similar to Academia.edu or ResearchGate, but more specific towards ...
1
vote
1answer
105 views

What do these contour maps tell me about my Collatz expression?

I tested this limit on WolframAlpha, $$ \lim_{t\to\infty}\frac {2\ 3^r (2 t - 1) - 6} {3\ 2^r (2 t - 1) - 6}=\left(\frac{3}{2}\right)^{r-1},$$ which displayed two contour maps: . Can ...
1
vote
0answers
103 views

Primality of Stirling numbers of second kind (again)

This question follows a previous one on the primality of Stirling numbers of the second kind ${n \brace k}$. Gerry indicated a paper on the topic. In this paper it is shown that for ${n \brace k}$ to ...
1
vote
0answers
44 views

Accounting for drop-outs in clinical trials

'Physical Therapy Review' [Intention to treat analysis, compliance, drop-outs and how to deal with missing data in clinical research: a review Susan Armijo-Olivo, Sharon Warren and David Magee Faculty ...
1
vote
1answer
101 views

Why zeta(2) in these inifinite sums?

The infinite sum of the reciprocals of these two sequences have zeta(2) in the result. The value is not in OEIS. A000326 A002411 Edit---rolled back the changes. Both $\frac{1}{2}$ and $2$ are ...