%I #7 Mar 30 2012 17:22:34

%S 4,6,7,8,11,13,15,19,21,23,25,27,37,39,41,45,51,55,57,63,69,73,75,81,

%T 87,93,99,105,111,117,123,135,147,153,159,165,171,195,201,213,219,225,

%U 231,237,243,255,267,273,285,297,315,321,363,369,399,405,411,423,435,447

%N Numbers n such that n-2^k is a prime or semiprime for all k > 0 with 2^k < n.

%C Is the sequence finite? If so, then A039669 is finite.

%H T. D. Noe, <a href="/A100349/b100349.txt">Table of n < 2^31</a>

%e 27 is here because 27-2 is a semiprime and 27-4, 27-8 and 27-16 are primes.

%t SemiPrimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; lst={}; Do[k=1; While[p=n-2^k; p>0 && (SemiPrimeQ[p] || PrimeQ[p]), k++ ]; If[p<=0, AppendTo[lst, n]], {n, 3, 1000}]; lst

%Y Cf. A039669 (n such that n-2^k is prime), A100350 (primes p such that p-2^k is prime or semiprime), A100351 (n such that n-2^k is semiprime).

%K nonn

%O 1,1

%A _T. D. Noe_, Nov 18 2004