Find the next 'n' Friday the 13ths in October that have a full moon

13.js

// Constants for the calculations
const SYNODIC_MONTH = 29.53058867; // Average lunar cycle in days (new moon to new moon)
const KNOWN_FULL_MOON = new Date(Date.UTC(2000, 0, 21, 4, 44)); // Known full moon date on 2000-01-21 04:44 UTC

/**
 * Returns the number of days from the known full moon date to the input date.
 * @param {Date} date
 * @returns {number} Number of days since known full moon
 */
function daysSince(date) {
    const msPerDay = 1000 * 60 * 60 * 24; // Convert milliseconds to days
    const diff = date - KNOWN_FULL_MOON;  // Difference from the known full moon
    return diff / msPerDay;               // Convert difference to days
}

/**
 * Determines if a given date has a full moon based on the full moon cycle.
 * @param {Date} date - The date to check
 * @returns {boolean} True if the date is within about a day of a full moon
 */
function isFullMoon(date) {
    const daysSinceKnownFullMoon = daysSince(date);
    const synodicAge = daysSinceKnownFullMoon % SYNODIC_MONTH;  // Age of the moon in terms of phase
    const distanceToFullMoon = Math.min(synodicAge, SYNODIC_MONTH - synodicAge); // Nearest distance to full moon
    return distanceToFullMoon < 1.0; // Close to a full moon within 1 day
}

/**
 * Function that finds Friday the 13ths in October with full moons
 */
function findFridayThe13thsWithFullMoon(n) {
    const results = [];
    let year = new Date().getFullYear(); // Start from the current year

    while (results.length < n) {
        for (let month = 0; month < 12; month++) {
            const day = new Date(year, month, 13);
            // Check for Friday the 13th in October
            if (day.getDay() === 5 && day.getMonth() === 9) { // 5 is Friday, 9 is October
                if (isFullMoon(day)) {
                    results.push(day);
                }
            }
        }
        year++;
    }

    return results;
}

// Find the next 3 Friday the 13ths in October with full moons
const result = findFridayThe13thsWithFullMoon(100);

result.forEach(date => {
    console.log(`Found a Friday the 13th with full moon on: ${date.toDateString()}`);
});