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A086006 Primes p such that 2*p-1 and 2*p+1 are semiprimes. 10

%I

%S 17,43,47,61,71,101,107,109,151,197,223,317,349,421,461,521,569,631,

%T 673,701,821,881,919,947,971,991,1051,1091,1109,1153,1181,1217,1231,

%U 1259,1321,1361,1367,1549,1693,1801,1847,1933,1951,1979,2143,2207

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

%C a(n) = A086005(n)/2.

%H T. D. Noe, <a href="/A086006/b086006.txt">Table of n, a(n) for n=1..10000</a>

%F A064911(2*a(n)-1) * A064911(2*a(n)+1) = 1. - _Reinhard Zumkeller_, Aug 08 2013

%e 101 is prime and 2*101-1=201=3*67, 2*101+1=203=7*29, therefore 101 is a term.

%e It is the sixth term and a(6)=101=A086005(6)/2.

%t Select[Prime[Range[400]],PrimeOmega[2#-1]==PrimeOmega[2#+1]==2&] (* _Harvey P. Dale_, Jun 23 2016 *)

%o (PARI) isok(n) = isprime(n) && (bigomega(2*n+1) == 2) && (bigomega(2*n-1) == 2) \\ _Michel Marcus_, Aug 01 2013

%o (Haskell)

%o a086006 = flip div 2 . a086005 -- _Reinhard Zumkeller_, Aug 08 2013

%Y Cf. A001358, A000040.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 07 2003

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)