# Questions tagged [sequence]

For challenges involving sequences, typically of numbers following some pattern.

944 questions
Filter by
Sorted by
Tagged with
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 ...
1k views

### Sums of X*Y chunks of the nonnegative integers

Consider the infinite table of the nonnegative integers with width 12: ...
• 9,251
564 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 ...
• 49.3k
219 views

### Non-Decreasing Fibonacci Sequence modulo M

Given integers $a,b,m, k, n$ and array $F = (f_1, f_2,...,f_n)$ defined as: \begin{cases} f_1 = \text{a}\\ f_2 = \text{b}\\ f_i = (f_{i-1} + f_{i-2}) \text{ mod m},∀i > 2 \end{cases} When $F$ ...
• 123
377 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 $a^{-1},b^{-1},c^{-1} ...$ . ...
• 41.6k
2k views

• 50.1k
1k views

### Repeating occupied pattern in Hilbert's hotel

Imagine a countable infinite amount of empty rooms. When an infinite amount of guests come, they occupy the 1st, 3rd, 5th...(all odd) empty rooms. Therefore there's always an infinite amount of empty ...
• 26k
2k views

### Make a k-skip-j range

On the Mathematica Stack Exchange, 100xln2 asks: I need a list of integers […] The list contains integers and is characterized by [three] parameters, lets call them k and j [and listmax], which ...
• 69k