2
votes
3answers
111 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: ...
11
votes
4answers
831 views

Integers which are the sum of both two and three consecutive squares

This is a math problem I came across the other day: I would like to know what would be a good way (esp. performance-wise) to check all first, lets say, 1000000, natural numbers if they can be ...
12
votes
1answer
263 views

the more effective method to find 21 digits armstrong number

In recreational number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number(after Michael F. Armstrong) or a plus perfect number) is a number that is ...
1
vote
1answer
251 views

Faster GCD Implementation

Is there any chance to write a faster GCD than the built-in one in Mathematica? @Mr.Wizard has written one in this question (although it's not for this purpose) which is 6 times slower on a 100k ...
14
votes
2answers
429 views

Why does iterating Prime in reverse order require much more time?

Say I would like to display the $10$ greatest primes that are less than $10^5$. I could do the following: ...
10
votes
2answers
464 views

FiniteFields package is very slow. Any fast substitute for Mathematica?

I want to compute the inverse of matrix, say with dimensions $100 \times 100$, defined over a large finite field extension such as $GF(2^{120})$. I am using the package FiniteFields, but Mathematica's ...
23
votes
1answer
3k views

Finding long strings of identical digits in transcendental numbers

Introduction Describing the three main streams of present-day mathematical philosophy (formalism, Platonism and intuitionism) in a well-known book, The Emperor's New Mind, R. Penrose says: ...it ...
23
votes
6answers
1k views

efficient way to count the number of zeros at the (right) end of a very large number

If I want to count the number of zeros at the (right) end of a large number, like $12345!$, I can use something like: Length[Last[Split[IntegerDigits[12345!]]]] ...