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7
votes
3answers
186 views

Find the number of $n$ such that $n!$ is a sum of three squares

I want to check the following theorem by using Mathematica: $\textbf{Theorem} $. $\text{The estimate}$ $\# \{n \le x:n! \text{ is a sum of three squares}\}=7x/8+O(x^{2/3})$ ...
2
votes
1answer
76 views

Unexpected behavior of FindGeneratingFunction

FindGeneratingFunction will give up to computer sometimes?Such as FindGeneratingFunction[{1, 4, 6, 4, 1}, x] But actually the ...
3
votes
0answers
42 views

Prepending a sequence with zeros gives `FindGeneratingFunction` hard time

Asking for FindGeneratingFunction[{1, 3, 11, 43, 171, 683, 2731, 10923, 43691, 174763}, t] gives the answer (namely ...
4
votes
3answers
77 views

Opposite Collatz Conjecture

I'm trying to explore what would happen if you change the collatz conjecture to flip the equations for odds and evens. So if you have an even number you multiply by 3, add 1, and divide by 2. If you ...
2
votes
1answer
47 views

FindInstance skips solutions

I have an equation to compute the bit-error rate of a binary symmetric channel: $$P_{err}(n,p) = \sum_{k = \frac{n-1}{2} + 1}^n\binom n k p^k(1-p)^{n-k}$$ I then want to find the smallest ...
1
vote
2answers
66 views

Engel expansion

How do I do an Engel expansion in Mathematica? And find the unique non-decreasing sequence of positive integers $ \{ a_1 ,a_2,a_3,\dots \}$ , such $$\frac{e}{\pi}=\frac{1}{a_1}+\frac{1}{a_1 ...
0
votes
1answer
52 views

How to calculate digits of Trott Constants?

How to calculate digits of numbers (Trott Constant) whose continued fraction representation is the same as the digits of its radix representation with Mathematica?
9
votes
2answers
129 views

Animating a growing ListPlot

I stumbled upon this (rather contrived but interesting) integer sequence. As it exhibits quite different behaviour at different scales, I would like to generate an animated ...
4
votes
2answers
349 views

How to plot the Fibonacci convergence to the golden ratio?

I am interested to plot a convergence result of the Fibonacci sequence, namely $\frac{F(n+1)}{F(n)}\rightarrow\phi$ as $n\rightarrow\infty$. So far I have created the following plot: So, I am ...
3
votes
2answers
75 views

How do I determine the 15th Lucas term in the 3rd order?

I want to implement the Lucas n-Step Number. This command taken from here doesn't seem to work, am I using the right command? ...
10
votes
9answers
2k views

How can I make a Tribonacci sequence in the form of a list?

How can I make a Tribonacci sequence that is in listing form? it suppose to look like the Fibonacci sequence but I couldn't get ...
6
votes
1answer
99 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 ...
2
votes
2answers
104 views

Building a sequence of the digits of π

Just for fun, I'm trying to write up some code that will list a finite number of the digits of pi, i.e. {3,1,4,1,5,...,#}. I have the general pattern, but for some ...
4
votes
2answers
241 views

Generate the Fibonacci sequence with Accumulate

Is there a way to generate the Fibonacci sequence with the Accumulate function?
21
votes
2answers
411 views

Speeding up the built-in Rudin-Shapiro and Thue-Morse sequence functions

Version 10.2 introduced two well-studied sequences as functions: the (Golay-)Rudin-Shapiro sequence (RudinShapiro[]) and the (Prouhet-)Thue-Morse sequence (...
2
votes
4answers
311 views

Print all numbers from a sequence which don't contain the digit 7

so i have this: Cases[RecurrenceTable[{a[n + 1] == 7 a[n] + n, a[1] == 1}, a, {n, 7}], Except[7]] But i noticed that it will only exclude numbers that are 7, and ...
0
votes
2answers
63 views

What would be the most efficient way of finding the first repeated term in Sylvester's sequence modulo the $n$th prime?

If a multiple of a prime, say 13, occurs in Sylvester's sequence, then Sylvester's sequence modulo that prime eventually gets stuck on a bunch of 1's, and ...
4
votes
2answers
232 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 ...
0
votes
1answer
50 views

How to condense many FindSequenceFunctions into a single one?

I have a function $f(n,k)$ that is rather large and complex, but if I hold $k$ constant and feed values into Mathematica over many $n$, I can get a closed-form expression for that $k$. However, I ...
0
votes
0answers
84 views

Strange behaviour if FindSequenceFunction

Consider a sequence starting with 2, subtract 2 to get the next term, now add 3 to get the next term and so on according to the rule (-2,+3) consecutively which starts like ...
3
votes
1answer
187 views

Interpreting a formula from Graph Theory - where do x and y come from?

I'm trying to understand the generating function for OEIS A062734, which is in Mathematica. Essentially, despite knowing no Mathematica at all, I think I can parse most of it, but where do $x$ and $y$ ...
8
votes
2answers
638 views

Finding the coefficient of a certain power in a generating function

I want to compute $(t^1+\dots +t^5)(t^2+\dots+ t^6)(t^3+\dots +t^9)$ and find the coefficient of $t^{15}$ for example. $t$ is an indeterminate Now in Maple this is simply as ...
8
votes
3answers
347 views

Is there a relatively quick way to solve my integer-valued equation?

This is a very simple problem. It can be solved by nested Forloops that exhaustively test every possible case, throwing out all non-solutions. Find all the ...
5
votes
1answer
235 views

More efficient Omnibus number determination?

Amusing myself with concepts from "Omnibus Sequences, Coupon Collection, and Missing Word Counts", in particular the sequences. To paraphrase the concept, a string is k-Omni over some alphabet a if ...
4
votes
3answers
1k views

How to test if all the elements in a list are Integers? [closed]

Consider a list such as s={1,2,3,3,5,6,3} With IntegerQ[number] , you know if number is an ...
2
votes
1answer
278 views

Using IntegerPartitions for distinct integers

What I would like to do is to find a way to test how many ways m distinct integers from the set {1,..., n} where ...
0
votes
1answer
82 views

Extend a function defined for integers to a differentiable function of a real variable

Here is a function that calculates the probability of randomly landing on a Fibonacci number not greater than $n$: ...
7
votes
5answers
4k 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 ...
12
votes
9answers
2k views

Fibonacci Sequence Generator

I'm trying to write a function in Workbench which will generate a Fibonacci sequence starting with F0 = 0 and F1 = 1. So far I ...
0
votes
1answer
68 views

Function that displays set of integers fulfilling constrictions

I would like to make a function of three parameters $i$, $j$ and $k$ that displays a list of integers fulfilling some criteria. Specifically the set of integers is: $\zeta_{ijk} = ...
1
vote
1answer
161 views

Find a sequence of integers which give max in each step

I would like to write a program in Mathematica to look for the integer $n$ such that the following definition holds for any $1 < m < n $ $$\frac{f(n)}{f(m)}>1+\frac{\log(n/m)}{\log(n) ...
10
votes
1answer
141 views

How do I expand StirlingS2[n, 10] in terms of elementary functions?

I know that it is possible to expand StirlingS2[n, 10] in terms of elementary functions of n. I tried ...
3
votes
1answer
287 views

How can I get the general term of this recurrence equations?

Following is the recurrence relation: a[1] = 1; a[n_] := a[n - a[n - 1]] + 1 Array[a, 28] I tried to use RSolve, but it ...
8
votes
2answers
2k views

Easier program for period of Fibonacci sequence modulo p

For a little project I need to calculate the period of a Fibonacci sequence modulo p, for which p is a prime number. For example, the Fibonacci sequence modulo 19 would be: $$0, 1, 1, 2, 3, 5, 8, 13, ...