Number Sequence ProblemDate: 08/11/97 at 14:58:54 From: Jon Mann Subject: Number sequence problem I have a number sequence but can not find out the pattern. Here are the numbers: 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, 167, 179, 181, 193, 223, 229, 233, 257, 263, 269, 313, 337, 367, 379, 383, 389, 419, 433, 461, 487, 491, 499, 503, 509, 541, 571, 577, ETC.... Dr. Math, you would be my hero if you got this sequence! J. M. Date: 08/15/97 at 15:04:54 From: Doctor Rob Subject: Re: Number sequence problem Dear J. M., This is an interesting question! Your sequence is the set of primes p for which 10 is a primitive root. Equivalently, this is the set of primes p for which p does not divide 10^k-1 for any k with 0 < k < p-1. Equivalently, this is the set of primes p for which 1/p has repeating decimal period of length p-1. 1/7 = .142857 142857 142857 ... period 6, 1/17 = .0588235294117647 0588235294117647 ... period 16, 1/19 = .052631578947368421 052631578947368421 ... period 18, etc. The length of the period must divide p-1, but is not always equal: 1/3 = .3 3 3 3 ... period 1 | 2 = 3-1, 1/11 = .09 09 09 ... period 2 | 10 = 11-1, 1/13 = .076923 076923 ... period 6 | 12 = 13-1, 1/31 = .032258064516129 032258064516129 ... period 15 | 30 = 31-1, etc. You can look up other sequences to find their rules by consulting the following URL: http://www.research.att.com/~njas/sequences/index.html There you can access a huge catalog of sequences online. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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