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A250288
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Numbers n such that the duodecimal repunit (12^n - 1)/11 is a semiprime.
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3
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7, 13, 17, 37, 47, 73, 101, 131, 151, 167, 197, 241, 263
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OFFSET
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1,1
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COMMENTS
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First unknown term is 311.
If (12^n - 1)/11 is a semiprime, n must be prime or the square of a prime (A001248), but no n = prime squared is known which yields a semiprime value of (12^n - 1)/11. (Specifically, n must be the square of a prime in A004064, and must be at least 491401 = 701^2.)
No other known terms below 1000; the only other possible terms below 1000 are 449, 521, 571, 577, 613, 709, 751, 757, 769, 787, 853, 859, 887, 929, and 991.
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LINKS
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EXAMPLE
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a(1) = 7 so 1111111 = 46E * 2X3E (written in base 12).
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MATHEMATICA
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Select[Range[120], PrimeOmega[(12^# - 1)/11] == 2 &] (* Alonso del Arte, Dec 18 2014 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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