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A086006 Primes p such that 2*p-1 and 2*p+1 are semiprimes.

%I A086006 #13 Jun 23 2016 10:30:59
%S A086006 17,43,47,61,71,101,107,109,151,197,223,317,349,421,461,521,569,631,
%T A086006 673,701,821,881,919,947,971,991,1051,1091,1109,1153,1181,1217,1231,
%U A086006 1259,1321,1361,1367,1549,1693,1801,1847,1933,1951,1979,2143,2207
%N A086006 Primes p such that 2*p-1 and 2*p+1 are semiprimes.
%C A086006 a(n) = A086005(n)/2.
%H A086006 T. D. Noe, <a href="/A086006/b086006.txt">Table of n, a(n) for n=1..10000</a>
%F A086006 A064911(2*a(n)-1) * A064911(2*a(n)+1) = 1. - _Reinhard Zumkeller_, Aug 08 2013
%e A086006 101 is prime and 2*101-1=201=3*67, 2*101+1=203=7*29, therefore 101 is a term.
%e A086006 It is the sixth term and a(6)=101=A086005(6)/2.
%t A086006 Select[Prime[Range[400]],PrimeOmega[2#-1]==PrimeOmega[2#+1]==2&] (* _Harvey P. Dale_, Jun 23 2016 *)
%o A086006 (PARI) isok(n) = isprime(n) && (bigomega(2*n+1) == 2) && (bigomega(2*n-1) == 2) \\ _Michel Marcus_, Aug 01 2013
%o A086006 (Haskell)
%o A086006 a086006 = flip div 2 . a086005  -- _Reinhard Zumkeller_, Aug 08 2013
%Y A086006 Cf. A001358, A000040.
%K A086006 nonn
%O A086006 1,1
%A A086006 _Reinhard Zumkeller_, Jul 07 2003