Euler001.fractran

# Project Euler 001 in FRACTRAN

## [The Problem](https://projecteuler.net/problem=1)

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get
3, 5, 6 and 9. The sum of these multiples is 23.

[below 20: 3, 5, 6, 9, 10, 12, 15, 18] 15 is in both

Find the sum of all the multiples of 3 or 5 below 1000.

## The Program

INPUT (n): 13^State Alpha One
OUTPUT:    7^sum

r2:          total
r3:          three
r5:          five
r7:          sum
r11:         temp
r13,r17:     State Alpha One and Two
r19,r23,r29: State Beta Three, Five, and ThreeAndFive
r31,r37:     State Gamma One and Two
r41,r43:     State Delta One and Two
r47:         end

### Pseudocode

while true {
    if (total >= 1000 && State Alpha One >= 1) {
        decrement total by 1000
        decrement alphaA
        increment end
    // State Alpha
    } else if (five >= 1 and three >= 1 and State Alpha One >= 1) {
        decrement three, five, and State Alpha One
        increment total and State Alpha Two
    } else if (State Alpha Two >= 1) {
        decrement State Alpha Two
        increment State Alpha One
    } else if (three >= 1 && State Alpha One >= 1) {
        decrement three and State Alpha One
        increment State Beta Three
    } else if (five >= 1 && State Alpha One >= 1) {
        decrement five and State Alpha One
        increment State Beta Five
    } else if (State Alpha One >= 1) {
        decrement State Alpha One
        State Beta ThreeAndFive
    // State Beta Three
    } else if (State Beta Three >= 1) {
        decrement State Beta Three
        increment five by 5
        increment three and State Gamma One
    // State Beta Five
    } else if (State Beta Five >= 1) {
        decrement State Beta Five
        increment three by 3
        increment five and State Gamma One
    // State Beta ThreeAndFive
    } else if (State Beta ThreeAndFive >= 1) {
        decrement State Beta ThreeAndFive
        increment three by 3
        increment five by 5
        increment State Gamma One
    // State Gamma
    } else if (total >= 1 && State Gamma One >= 1) {
        decrement total and State Gamma One
        increment sum, temp, and State Gamma Two
    } else if (State Gamma Two >= 1) {
        decrement State Gamma Two
        increment State Gamma One
    } else if (State Gamma One >= 1) {
        decrement State Gamma One
        increment State Delta One
    // State Delta
    } else if (temp >= 1 && State Delta One >= 1) {
        decrement temp and State Delta One
        increment total and State Delta Two++
    } else if (State Delta Two >= 1) {
        decrement State Delta Two
        increment State Delta One
    } else if (State Delta One >= 1) {
        decrement State Delta One
        increment State Alpha One
    } else {
        break
    }
}

## FRACTRAN Pseudocode

(
    47 / 2^1000 * 13,
    17 / 3 * 5 * 13,
    13 / 17,
    19 / 3 * 13,
    23 / 5 * 13,
    29 / 13,
    3 * 5^5 * 31 / 19,
    3^3 * 5 * 31 / 23,
    3^3 * 5^5 * 31 / 29,
    7 * 11 * 37 / 2 * 31,
    31 / 37,
    41 / 31,
    2 * 43 / 11 * 41,
    41 / 43,
    13 / 41
)

// Expanded

(
    47 / 2^1000 * 13,
    17 / 195,
    13 / 17,
    19 / 39,
    23 / 65,
    29 / 13,
    290,625 / 19,
    4185 / 23,
    2,615,625 / 29,
    2849 / 62,
    31 / 37,
    41 / 31,
    86 / 451,
    41 / 43,
    13 / 41
)


## Possible Improvements