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%I #27 Sep 08 2022 08:46:06
%S 7,17,19,43,47,59,61,71,79,101,107,109,149,151,163,167,197,223,257,
%T 263,271,311,317,347,349,353,383,389,401,421,439,449,461,479,503,521,
%U 523,557,569,599,601,613,631,673,677,691,701,811,821,827,839,853,863,881
%N Primes p such that 2*p + 1 is semiprime.
%C Also primes of the form (p*q - 1)/2, where p and q are distinct primes.
%H Harvey P. Dale, <a href="/A234095/b234095.txt">Table of n, a(n) for n = 1..1000</a>
%F 2*a(n)+1 = A233561(n). - _R. J. Mathar_, Aug 30 2016
%e 7 is in the sequence because it is prime and 7*2 + 1 = 15 = 3*5 is a semiprime.
%t t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
%t v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A233561 *)
%t (w - 1)/2 (* A234095 *) (* _Peter J. C. Moses_, Dec 23 2013 *)
%t Select[Prime[Range[200]],PrimeOmega[2#+1]==2&] (* _Harvey P. Dale_, Mar 19 2015 *)
%o (PARI) is(n)=isprime(n) && bigomega(2*n+1)==2 \\ _Charles R Greathouse IV_, Feb 19 2014
%o (Magma) IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(1000)| IsSemiprime(2*p+1)]; // _Vincenzo Librandi_, Feb 21 2014
%Y Cf. A233561, A234096, A233562.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Dec 27 2013
%E New name from _Zak Seidov_, Feb 19 2014
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