A234098 - OEIS

%I #8 Dec 04 2016 19:46:33

%S 11,17,29,43,47,67,71,73,89,101,103,107,109,127,151,191,197,223,227,

%T 241,251,269,277,283,317,349,359,373,397,409,433,457,461,467,487,521,

%U 541,569,571,631,643,647,659,673,701,709,719,733,739,751,757,769,821

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

%H Reinhard Zumkeller, <a href="/A234098/b234098.txt">Table of n, a(n) for n = 1..10000</a>

%e 11 = (3*7 + 1)/2, 17 = (5*7 + 1)/2.

%t t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t + 1)/2, 120] (* A234096 *)

%t v = Flatten[Position[PrimeQ[(t + 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}]  (* A233562 *)

%t (w + 1)/2 (* A234098 *)  (* _Peter J. C. Moses_, Dec 23 2013 *)

%o (Haskell)

%o a234098 n = a234098_list !! (n-1)

%o a234098_list = filter ((== 1) . a010051') $

%o                       map ((flip div 2) . (+ 1)) a046388_list

%o -- _Reinhard Zumkeller_, Jan 02 2014

%Y Cf. A234096, A233562, A234095.

%Y Cf. A010051, A046388.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Dec 27 2013