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A176351
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Numbers n such that 2*3^n + 1 is a primitive prime factor of 10^3^n - 1.
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0
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OFFSET
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1,1
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COMMENTS
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Consider the problem of finding the smallest number k such that the decimal representation of 1/k has period 3^e for a given e. The number k is usually 3^(e+2). However, if e is one of the n in this sequence, then the prime 2*3^n+1 is a smaller k. The first instance of these exceptions is 1/163, which has a period of 81.
10 must be a square residue modulo 2*3^n + 1, implying that n must be a multiple of 4.
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LINKS
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MATHEMATICA
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Select[Range[10000], PrimeQ[1+2*3^# ] && MultiplicativeOrder[10, 1+2*3^# ] == 3^# &]
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CROSSREFS
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Cf. A003306 (primes of the form 2*3^n+1), A003060 (least k such that 1/k has period n).
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KEYWORD
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hard,more,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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