Rust

After spending most of my life learning and trying to master C++, I have recently decided to give Rust a try. I only have one project, but I really enjoy the language thus far.

fn main() {
    let n = 5;
    
    if n < 0 {
        print!("{} is negative", n);
    } else if n > 0 {
        print!("{} is positive", n);
    } else {
        print!("{} is zero", n);
    }
}

Lucky Numbers

Lucky Numbers are a concept introduced to me by one of my professors Dr. Duane Skaggs. And one of the first Rust projects that I have worked on, but before I get to the rust code, I should explain what lucky numbers are.

Also…

Therefore 11 is a lucky number. In general, a lucky number is any integer which can be expressed as the sum of integers whose reciprocals add to one.

Take a moment to find some lucky numbers on your own. This dropdown contains the first 11

$1, 4, 9, 10, 11, 16, 18, 20, 22, 24, 25$

These are the first 11 lucky numbers. One of these numbers actually has 3 unique constructions.

Doubly Lucky Numbers

Some numbers have multiple have multiple ways to construct them in a lucky way, take 31 for example:

31 has two constructions, in this case we would say it has a luckiness of 2

Finding Lucky Numbers

I believe that there are many ways to find lucky numbers, however the that I found works by starting with a common denominator and constructing lucky numbers from that number.

For example, with the number 4 as a common denominator, you can find the following fractions which add to 1

These correspond to the lucky numbers of 16 and 10, and it gives their construction by simplifying the fractions.

Rust Console Application

I made a repo with the following 4 functionalities

is_lucky

Prints if a number in a range is lucky

$ luckynums is_lucky 10 25
10: true
11: true
12: false
13: false
14: false
15: false
16: true
17: false
18: true
19: false
20: true
21: false
22: true
23: false
24: true
25: true

luckiness

Prints the luckiness of a number in a given range

$ luckynums luckiness 1 35
1: 1
2: 0
3: 0
4: 1
5: 0
6: 0
7: 0
8: 0
9: 1
10: 1
11: 1
12: 0
13: 0
14: 0
15: 0
16: 1
17: 0
18: 1
19: 0
20: 1
21: 0
22: 3
23: 0
24: 1
25: 1
26: 0
27: 1
28: 1
29: 1
30: 1
31: 2
32: 1
33: 2
34: 1
35: 1

constructions

Prints the constructions for lucky numbers in a given range

$ luckynums constructions 1 35
1:      1
2 [Not Lucky]
3 [Not Lucky]
4:      2*2
5 [Not Lucky]
6 [Not Lucky]
7 [Not Lucky]
8 [Not Lucky]
9:      3*3
10:     4*2 + 2
11:     6 + 3 + 2
12 [Not Lucky]
13 [Not Lucky]
14 [Not Lucky]
15 [Not Lucky]
16:     4*4
17 [Not Lucky]
18:     6*2 + 3*2
19 [Not Lucky]
20:     6*3 + 2
21 [Not Lucky]
22:     8*2 + 4 + 2
        10 + 5*2 + 2
        12 + 4 + 3*2
23 [Not Lucky]
24:     12 + 6 + 4 + 2
25:     5*5
26 [Not Lucky]
27:     6*4 + 3
28:     8*2 + 4*3
29:     12*2 + 3 + 2
30:     12 + 6 + 4*3
31:     12 + 6*2 + 4 + 3
        20 + 5 + 4 + 2
32:     18 + 9 + 3 + 2
33:     9*3 + 3*2
        15 + 5*3 + 3
34:     8*4 + 2
35:     12*2 + 4*2 + 3

plot

Outputs a graph to chart.png using the plotters crate

$ luckynums plot 1 50
Results saved to chart.png

Chart.png: