Algosim documentation: SequenceList

SequenceList

Returns a list with an arithmetic sequence of integers.

Syntax

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

See also