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Unformatted text preview: University of California San Diego ECE15: Engineering Computation Final Exam: Problem # 4 The digital root of a positive integer N is computed as follows. First, N is written-out in the decimal number system, and its digits are summed up to produce the number N 1 . Then the decimal digits of N 1 are summed to produce the number N 2 . And so on. The process continues until we obtain a single-digit decimal number, namely one of 1, 2, 3, 4, 5, 6, 7, 8, 9 . This single-digit decimal number is the digital root of N . For example, the computation of the digital root of the integer N 2 31 proceeds as follows: 2 31 2147483648 2 1 4 7 4 8 3 6 4 8 47 4 7 11 1 1 2 In this problem, we are interested in a variation on this theme, which we call the prime digital root . The prime digital root of a positive integer N is computed using the same process as above, except that the process stops either when a single-digit number is reached or when a prime number is reached. Thus if N is prime, then the prime digital root of N is N itself. On the other hand, if the process reaches a single-digit number which is not prime, namely one of 1, 4, 6, 8, 9 , then we say that...
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- Fall '08