All Questions
874
questions
5
votes
5
answers
252
views
Fractions nobody needs (because they can be reduced to a simpler form)
It happened in the 19th century. Georg was bored and started counting the rational numbers. Surprisingly, he discovered that there were no more of them than natural numbers. This insight made Georg ...
- 511
18
votes
11
answers
2k
views
Count squares in my pi approximation
One way to approximate π is the following: Start by drawing a 2x2 square with a quarter-circle in it. Then, the area of the quarter-circle is π.
We can approximate this area by filling it with ...
- 42.4k
11
votes
10
answers
2k
views
Smallest prime q such that concatenation (p+q)"q is a prime
Let p, q, and c := (p + q)"q (where " denotes concatenation) be positive integers such that p and c are primes and q is the smallest prime such that c is prime.
Such a prime triple (p, q, (p ...
- 511
15
votes
10
answers
1k
views
Sylvester primes
Sylvester's sequence can be defined recursively S(n) = S(n-1)*(S(n-1) + 1) for n >= 1 starting S(0) = 1.
Since S(n) and S(n) + 1 have no common divisors, it follows that S(n) has at least one more ...
- 511
15
votes
15
answers
1k
views
Sums of X*Y chunks of the nonnegative integers
Consider the infinite table of the nonnegative integers with width 12:
...
- 9,321
14
votes
16
answers
573
views
Rabinowitz-Wagon \$\pi\$ formula
In 1995, Stanley Rabinowitz and Stan Wagon found an interesting algorithm to generate the digits of \$\pi\$ one by one without storing the previous results. The algorithm is called the spigot ...
- 49.4k
14
votes
5
answers
382
views
Generate a subgroup of a free group
In group theory, the free group with \$n\$ generators can be obtained by taking \$n\$ distinct symbols (let's call them \$a, b, c ...\$ etc), along with their inverses \$ a^{-1},b^{-1},c^{-1} ...\$ . ...
- 42.4k
17
votes
24
answers
2k
views
Smallest Harmonic number greater than N
The sequence of Harmonic numbers are the sums of the reciprocals of the first k natural numbers (not including zero):
\${\displaystyle H_{k}=1+{\frac {1}{2}}+{\frac {1}{3}}+\cdots +{\frac {1}{k}}=\sum ...
- 9,321
18
votes
18
answers
1k
views
15
votes
2
answers
400
views
Where are zeros? Self-describing sequence
Background
A167519: Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.
...
- 78.2k
16
votes
6
answers
1k
views
Golfing the complexity with subtraction
The Mahler-Popken complexity, \$C(N)\$, of a positive integer, \$N\$, is the smallest number of ones (\$1\$) that can be used to form \$N\$ in a mathematical expression using only the integer* \$1\$ ...
- 109k
13
votes
11
answers
805
views
*Trivial* near-repdigit perfect powers
Task
Output the sequence that precisely consists of the following integers in increasing order:
the 2nd and higher powers of 10 (\$10^i\$ where \$i \ge 2\$),
the squares of powers of 10 times 2 or 3 (...
- 78.2k
14
votes
10
answers
1k
views
Enumerate all matches of a regex
related
For this challenge, we'll be using a simplified dialect of regular expressions, where:
A lowercase letter from a to z ...
- 42.4k
10
votes
4
answers
2k
views
Output a 1-2-3-5-7... sequence
Follow-up of my previous challenge, inspired by @emanresu A's question, and proven possible by @att (Mathematica solution linked)
For the purposes of this challenge, a 1-2-3-5-7... sequence is an ...
- 2,143
21
votes
15
answers
2k
views
Output a 1-2-3 sequence
For the purposes of this challenge, a 1-2-3 sequence is an infinite sequence of increasing positive integers such that for any positive integer \$n\$, exactly one of \$n, 2n,\$ and \$3n\$ appears in ...
- 2,143