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A234098 Primes of the form (p*q + 1)/2, where p and q are distinct primes.

%I A234098 #10 Jun 24 2025 15:58:36
%S A234098 11,17,29,43,47,67,71,73,89,101,103,107,109,127,151,191,197,223,227,
%T A234098 241,251,269,277,283,317,349,359,373,397,409,433,457,461,467,487,521,
%U A234098 541,569,571,631,643,647,659,673,701,709,719,733,739,751,757,769,821
%N A234098 Primes of the form (p*q + 1)/2, where p and q are distinct primes.
%H A234098 Reinhard Zumkeller, <a href="/A234098/b234098.txt">Table of n, a(n) for n = 1..10000</a>
%e A234098 11 = (3*7 + 1)/2, 17 = (5*7 + 1)/2.
%t A234098 t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t + 1)/2, 120] (* A234096 *)
%t A234098 v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A233562 *)
%t A234098 (w + 1)/2 (* A234098 *)  (* _Peter J. C. Moses_, Dec 23 2013 *)
%t A234098 Take[Select[(Times@@#+1)/2&/@Subsets[Prime[Range[200]],{2}],PrimeQ]//Union,60] (* _Harvey P. Dale_, Jun 24 2025 *)
%o A234098 (Haskell)
%o A234098 a234098 n = a234098_list !! (n-1)
%o A234098 a234098_list = filter ((== 1) . a010051') $
%o A234098                       map ((flip div 2) . (+ 1)) a046388_list
%o A234098 -- _Reinhard Zumkeller_, Jan 02 2014
%Y A234098 Cf. A234096, A233562, A234095.
%Y A234098 Cf. A010051, A046388.
%K A234098 nonn,easy
%O A234098 1,1
%A A234098 _Clark Kimberling_, Dec 27 2013