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%I #11 Jul 11 2015 16:34:37
%S 15,63,511,1023,16383,32767,2097151,4194303,33554431,67108863,
%T 8589934591,17179869183,34359738367,274877906943,549755813887,
%U 70368744177663,562949953421311,2251799813685247,36028797018963967
%N 2^(n-th semiprime) - 1.
%C This is a semiprime analog of A001348 Mersenne numbers. The semiprimes in this sequence are the analogs of A000668 Mersenne primes (of form 2^p - 1 where p is a prime). a(n) is semiprime when a(n) is an element of A092561, which happens for values of n beginning 1, 3, 17, which is A085724 INTERSECTION A001358 and has no more values under 1000. Would someone like to extend the latter set of indices j of semiprimes k = A001358(j) such that (2^k)-1 is semiprime?
%F a(n) = (2^A001358(n))-1.
%e a(1) = (2^4) - 1 = 15 because 4 is the 1st semiprime. Note that 15 = 3*5 is itself semiprime.
%e a(2) = (2^6) - 1 = 63 because 6 is the 2nd semiprime. Note that 63 = (3^2)*7 is not itself semiprime.
%e a(3) = (2^9) - 1 = 511 because 9 is the 3rd semiprime; and 511 = 7 * 73 is itself semiprime.
%e a(17) = (2^17)-1 = 562949953421311 = 127 * 4432676798593, itself semiprime.
%t 2^#-1&/@Select[Range[100],PrimeOmega[#]==2&] (* _Harvey P. Dale_, Jun 26 2011 *)
%Y Cf. A000668, A001348, A001358, A085724, A092561.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, May 03 2008
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