My Java solution:

public static String dayOfProgrammer(int year) {
    StringBuffer buf = new StringBuffer();
    int day = 13;

    if (year == 1918) {
        day = 26;
    } else if (year < 1918) {
        if (isJulianLeapYear(year)) day-=1;
    } else if (year > 1918) {
        if (isGregorianLeapYear(year)) day-=1;
    }

    buf.append(day + ".09." + year);

    return buf.toString();
}

private static boolean isJulianLeapYear(int year) {
    if (year % 4 == 0) return true;
    return false;
}

private static boolean isGregorianLeapYear(int year) {
    if ((year % 400 == 0) || (year % 4 == 0 && year % 100 != 0)) return true;
    return false;
}