﻿ SequenceList – Algosim documentation
Algosim documentation: SequenceList

# SequenceList

Returns a list with an arithmetic sequence of integers.

## Syntax

• `SequenceList(n)`

• `n` is a positive integer

• `SequenceList(a, b[, d])`

• `a` and `b` are integers

• `d` is a positive integer

## Description

If `n` is a positive integer, then `SequenceList(n)` returns the list containing the first `n` positive numbers in order.

If `a` and `b` are integers, then `SequenceList(a, b)` returns the list containing all integers from `a` to `b` (inclusively) in order. If `b < a`, the sequence is decreasing. `SequenceList(a, b, k)` returns the integers from `a` to `b` with step `k`, that is, the integers `a, a ± k, a ± 2k, ... ` in the direction of `b` but never exceeding `b`.

## Examples

`SequenceList` is often used to generate arbitrary sequences by means of the `@` operator and function objects:

`SequenceList(10) @ sqr`
```1
4
9
16
25
36
49
64
81
100
```
`SequenceList(10) @ prime`
```2
3
5
7
11
13
17
19
23
29
```
`SequenceList(10) @ (n ↦ 2⋅n^2 − 1)`
```1
7
17
31
49
71
97
127
161
199
```
`ℙ ≔ SequenceList(1000000) @ prime;`
`count(ℙ, p ↦ ∑(digits(p)) = 10)`
`1121`

Another approach is to use the `compute` function:

`compute(n!, n, 1, 10)`
```1
2
6
24
120
720
5040
40320
362880
3628800
```