We have several question asking about book recommendations for general topology - for example the posts linked to Best book for topology? or the posts mentioned in the relevant section of http://meta.math.stackexchange.com/questions/1868/list-of-generalizations-of-common-questions. These posts r...
the self-counting problem is to find a turing machine that compute the following function
$$
\begin{align*}
f(m) &=
\begin{cases}
m & \text{if turing machine $m$ halts on input $m$ after $m$ steps with output $m$} \\
0 & \text{otherwise} \\
\end{cases}
\end{align*}
$$
you must ...
The Riemann R function is as follows:
$$R (x)=\sum _{n=1}^{\infty } \frac{\mu (n) \text{li}\left(x^{1/n}\right)}{n}.$$
This uses the Möbius function as well as the logarithmic integral.
From the wikipedia, the Möbius function is defined so that for any positive integer \$n\$, \$μ(n)\$ is the sum...
Challenge
Given an integer, \$s\$, as input where \$s\geq 1\$ output the value of \$\zeta(s)\$ (Where \$\zeta(x)\$ represents the Riemann Zeta Function).
Further information
\$\zeta(s)\$ is defined as:
$$\zeta(s) = \sum\limits^\infty_{n=1}\frac{1}{n^s}$$
You should output your answer to 5 de...
From time to time, answers can be posted to the site which, at the time are valid but later become invalid without any fault of the original answerer. For example, a number of answers to this challenge use domains such as http://ppcg.lol and http://ppcg.ga, which, at the time, worked, but have si...
Introduction
The \$RADD(n)\$ operation is defined as the sum of \$n + [\$ the number whose decimal representation are the decimal digits of \$n\$ in reverse order \$]\$, see A004086. After reversal, trailing zeros are lost. See Reverse-Then-Add Sequence and A056964.
Not all numbers can be represe...
Python 3.8
I wrote this janky code a long time ago based on some blogpost about Meissel-Lehmer I read. I'm not even sure how it works any more. One day I'll get around to cleaning it up and optimizing it.
Unofficial timing for 1907000000 case is 0.98 sec.
def memoize(obj):
"""Decorator that m...
