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A367648
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Primes p such that the multiplicative order of 3 modulo p is a power of 3.
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2
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2, 13, 109, 433, 757, 3889, 8209, 17497, 52489, 58321, 70957, 1190701, 1705861, 2598157, 6627097, 13463173, 57395629, 23245229341, 79320757897
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OFFSET
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1,1
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COMMENTS
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Prime factors of numbers of the form 3^3^i - 1: p divides 3^3^i - 1 if and only if the multiplicative order of 3 modulo p is a power of 3 not exceeding 3^i.
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LINKS
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EXAMPLE
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13 is a term since the multiplicative order of 3 modulo 13 is 3 = 3^1, which means that 13 is a factor of 3^3^1 - 1.
109 is a term since the multiplicative order of 3 modulo 109 is 27 = 3^3, which means that 109 is a factor of 3^3^3 - 1.
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PROG
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(PARI) isA367648(n) = isprime(n) && (n!=3) && isprimepower(3*znorder(Mod(3, n)))
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CROSSREFS
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Cf. A367649 (ord(3,p) being 2 times a power of 3, prime factors of numbers of the form 3^3^i + 1), A023394 (ord(2,p) being a power of 2, prime factors of numbers of the form 2^2^i - 1 (or of the form 2^2^i + 1)).
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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