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%I #3 Mar 30 2012 17:22:34
%S 7,11,13,19,23,37,41,73
%N Primes p such that p-2^k is a prime or semiprime for all k > 0 with 2^k < p.
%C These are the primes in A100349. No others < 10^9; conjecture that this sequence is finite.
%e 37 is here because 37-2, 37-4, 37-16 are semiprimes and 37-8, 37-32 are primes.
%t SemiPrimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; lst={}; Do[k=1; While[n=Prime[i]; p=n-2^k; p>0 && (SemiPrimeQ[p] || PrimeQ[p]), k++ ]; If[p<=0, AppendTo[lst, n]], {i, 2, 1000}]; lst
%Y Cf. A039669 (n such that n-2^k is prime), A100349 (n such that n-2^k is prime or semiprime), A100351 (n such that n-2^k is semiprime).
%K more,nonn
%O 1,1
%A _T. D. Noe_, Nov 18 2004
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