
    Design an algorithm to determine the monitoring interval (in hours) for a patient at risk level n, where intervals follow a specialized medical sequence that helps predict readmission risk. Each interval in this sequence is calculated using the previous two intervals' values, starting with 1 and 1, where each new interval equals the sum of its predecessor plus twice the value two positions before it, and only prime numbers in this sequence are used as valid monitoring periods.
    

    
def newman_prime(n):
    """
    Design an algorithm to determine the monitoring interval (in hours) for a patient at risk level n, where intervals follow a specialized medical sequence that helps predict readmission risk. Each interval in this sequence is calculated using the previous two intervals' values, starting with 1 and 1, where each new interval equals the sum of its predecessor plus twice the value two positions before it, and only prime numbers in this sequence are used as valid monitoring periods.
    

    """
def newman_prime(n):
    """
    Design an algorithm to determine the monitoring interval (in hours) for a patient at risk level n, where intervals follow a specialized medical sequence that helps predict readmission risk. Each interval in this sequence is calculated using the previous two intervals' values, starting with 1 and 1, where each new interval equals the sum of its predecessor plus twice the value two positions before it, and only prime numbers in this sequence are used as valid monitoring periods.
    

    """
    if n == 0 or n == 1:
        return 1
    return 2 * newman_prime(n - 1) + newman_prime(n - 2)