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%I #25 Dec 24 2014 23:29:43
%S 7,13,17,37,47,73,101,131,151,167,197,241,263
%N Numbers n such that the duodecimal repunit (12^n - 1)/11 is a semiprime.
%C First unknown term is 311.
%C 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.)
%C 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.
%H Samuel Wagstaff, <a href="http://www.cerias.purdue.edu/homes/ssw/cun/index.html">The Cunningham Project</a>
%e a(1) = 7 so 1111111 = 46E * 2X3E (written in base 12).
%t Select[Range[120], PrimeOmega[(12^# - 1)/11] == 2 &] (* _Alonso del Arte_, Dec 18 2014 *)
%Y Cf. A046413, A085724, A004064.
%K nonn,more
%O 1,1
%A _Eric Chen_, Dec 18 2014
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